Cluster-Based Data Aggregation in Flying Sensor Networks Enabled Internet of Things

Abstract

Multiple unmanned aerial vehicles (UAVs) are organized into clusters in a flying sensor network (FSNet) to achieve scalability and prolong the network lifetime. There are a variety of optimization schemes that can be adapted to determine the cluster head (CH) and to form stable and balanced clusters. Similarly, in FSNet, duplicated data may be transmitted to the CHs when multiple UAVs monitor activities in the vicinity where an event of interest occurs. The communication of duplicate data may consume more energy and bandwidth than computation for data aggregation. This paper proposes a honey-bee algorithm (HBA) to select the optimal CH set and form stable and balanced clusters. The modified HBA determines CHs based on the residual energy, UAV degree, and relative mobility. To transmit data, the UAV joins the nearest CH. The re-affiliation rate decreases with the proposed stable clustering procedure. Once the cluster is formed, ordinary UAVs transmit data to their UAVs-CH. An aggregation method based on dynamic programming is proposed to save energy consumption and bandwidth. The data aggregation procedure is applied at the cluster level to minimize communication and save bandwidth and energy. Simulation experiments validated the proposed scheme. The simulation results are compared with recent cluster-based data aggregation schemes. The results show that our proposed scheme outperforms state-of-the-art cluster-based data aggregation schemes in FSNet.

Full text

Citation: Salam, A.; Javaid, Q.;
Ahmad, M.; Wahid, I.; Arafat, M.Y.
Cluster-Based Data Aggregation in
Flying Sensor Networks Enabled
Internet of Things. Future Internet
2023,15, 279. https://doi.org/
10.3390/fi15080279
Academic Editor: Claude Chaudet
Received: 31 July 2023
Revised: 16 August 2023
Accepted: 18 August 2023
Published: 20 August 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
future internet
Article
Cluster-Based Data Aggregation in Flying Sensor Networks
Enabled Internet of Things
Abdu Salam 1, Qaisar Javaid 2, Masood Ahmad 1, Ishtiaq Wahid 1and Muhammad Yeasir Arafat 3, *
1Department of Computer Science, Abdul Wali Khan University, Mardan 23200, Pakistan;
abdusalam@awkum.edu.pk (A.S.); masood@awkum.edu.pk (M.A.); ishtiaqwahid@awkum.edu.pk (I.W.)
2Department of Computer Science and Software Engineering, International Islamic University,
Islamabad 44000, Pakistan; qaisar@iiu.edu.pk
3IT Research Institute, Chosun University, 309 Pilmun-daero, Dong-gu, Gwangju 61452, Republic of Korea
*Correspondence: myarafat@chosun.ac.kr
Abstract:
Multiple unmanned aerial vehicles (UAVs) are organized into clusters in a flying sensor
network (FSNet) to achieve scalability and prolong the network lifetime. There are a variety of
optimization schemes that can be adapted to determine the cluster head (CH) and to form stable and
balanced clusters. Similarly, in FSNet, duplicated data may be transmitted to the CHs when multiple
UAVs monitor activities in the vicinity where an event of interest occurs. The communication of
duplicate data may consume more energy and bandwidth than computation for data aggregation.
This paper proposes a honey-bee algorithm (HBA) to select the optimal CH set and form stable and
balanced clusters. The modified HBA determines CHs based on the residual energy, UAV degree,
and relative mobility. To transmit data, the UAV joins the nearest CH. The re-affiliation rate decreases
with the proposed stable clustering procedure. Once the cluster is formed, ordinary UAVs transmit
data to their UAVs-CH. An aggregation method based on dynamic programming is proposed to save
energy consumption and bandwidth. The data aggregation procedure is applied at the cluster level
to minimize communication and save bandwidth and energy. Simulation experiments validated the
proposed scheme. The simulation results are compared with recent cluster-based data aggregation
schemes. The results show that our proposed scheme outperforms state-of-the-art cluster-based data
aggregation schemes in FSNet.
Keywords:
clustering; data aggregation; dynamic programming; flying sensor network; internet
of things
1. Introduction
A multi-unmanned aerial vehicle (UAV)-aided flying sensor network (FSNet) is con-
strained by various energy factors, such as limited energy, computation, memory, and
communication [
1
,
2
]. The energy consumption for sensing and computation is less than the
energy used for communication among the UAVs or to the ground station (GS) [
3
,
4
]. The
available energy resources are sometimes insufficient for transmission and computation
during the mission. However, the collected data need to be communicated to the destina-
tion for further processing. The performance of the network lifetime depends on efficient
energy utilization [
5
]. The researchers tried to minimize energy utilization in other wireless
networks, but energy utilization still exists. Due to the flying speed of UAVs, the rapid
variation in topology, terrain structure, and diverse directions make it difficult to collect
and route information [
6
]. The researchers proposed energy-efficient schemes by consider-
ing different parameters such as reducing the communication distance, computation cost,
mobility, and degree. However, data collection and minimization of communication load
go unnoticed to save bandwidth and energy [7,8].
A data aggregation approach reduces the energy consumption of UAVs and increases
their lifespan. The data aggregation approach is different in wireless sensor networks
Future Internet 2023,15, 279. https://doi.org/10.3390/fi15080279 https://www.mdpi.com/journal/futureinternet

Future Internet 2023,15, 279 2 of 24
(WSNs) and vehicular ad hoc networks (VANETs) from UAV networks [
9
]. In WSN, the
uses of the data aggregation approach are for decreasing energy consumption rather than
minimizing network capacity usage [
10
]. In VANET, due to the high variation in the topol-
ogy, data aggregation is performed by many vehicles. In addition to the degree, mobility,
density, and other parameters, the multi-UAV system is constrained by energy factors,
which is why it is compatible with WSN and VANET requirements [
11
]. UAVs also consume
energy by processing and storing more data, just like flight and communication [12].
UAV-based data aggregation has emerged as a promising solution for collecting data
from remote and hard-to-reach areas. One of the main motivations for UAV-based data
aggregation is the ability to obtain data more efficiently and accurately. UAVs can cover a
larger area in a shorter amount of time compared to traditional data collection methods.
This means that data can be collected faster, allowing for a quicker analysis and quicker
decision-making. Additionally, UAV-based data aggregation can also reduce data collection
costs. Traditional methods often require expensive equipment and personnel, whereas
UAVs can be operated by a single person and require minimal equipment.
The fundamental operation in FSNet is data aggregation, which aims to transmit data
among UAVs or to the GS. The data aggregation approach reduces communication costs
and bandwidth utilization while obtaining aggregated data. Data aggregation utilizes the
concept of many-to-few. A data aggregation protocol describes how the data are gathered,
how they are routed to the destination, and when they should be transmitted.
Therefore, in this study, we developed a cluster-based data aggregation scheme for
UAV-based FSNet. This research contributes the following:
•
An effective mechanism designed based on a honey-bee algorithm (HBA) to select
optimal unmanned aerial vehicles–cluster head (UAVs-CH).
•The formation of balanced and stable clusters reduces re-affiliation rates.
•
Data aggregation algorithm proposed to limit duplicated data communication to the
base station (BS).
•Avoids the transmission of unwanted packets to the BS and save FSNet bandwidth.
•
Mathematical techniques measure the accuracy and correctness of the proposed scheme.
The remaining article is structured as follows: Section 2elaborates on the existing
literature. Section 3discusses the proposed cluster formation and data aggregation schemes.
In Section 4, experiment evaluation and simulation outcomes are outlined. In the Section 6,
the paper concludes and states future directions.
2. Background
This section reviews the existing work on energy-efficient clustering and UAV-based
data aggregation approaches. A UAV-based data aggregation network architecture dif-
fers significantly from a traditional wireless sensor network. For these reasons, existing
algorithms for stationary or low-mobility WSNs are not feasible [
13
]. A data aggrega-
tion algorithm based on UAVs needs to be able to adapt to networks with high mobility,
sudden changes in topology, and sporadic communication links. WSNs require different
levels of quality of service, including delay, packet loss, and reliability on the underlying
networks. Furthermore, WSNs are limited in terms of energy, computation power, and
network resources. An appropriate data aggregation technique is essential for meeting
requirements while respecting WSN limitations. WSNs require time synchronization to
coordinate data, energy, and localization. To address the sensor time synchronization
problem, the authors of [
14
] proposed a pairwise broadcast synchronization (PBS) protocol
for multi-cluster sensor networks that reduces overall energy consumption while maintain-
ing synchronization accuracy. Reference [
15
] proposed a distributed heuristic algorithm
for selecting appropriate sensors in a multi-hop sensor network to reduce the number of
message exchanges needed for network-wide synchronization using PBS.

Future Internet 2023,15, 279 3 of 24
2.1. Energy Efficient Clustering
Energy-efficient clustering strategies for FSNet are still in their infancy [
16
]. This
section presents an overview of some existing energy-efficient solutions based on different
parameters, criteria, and approaches. FSNet has many military and civil applications.
Nevertheless, the main issues of UAVs in FSNet are limited energy, high mobility, fre-
quent topology changes, and terrain structure, due to the limited flight time of UAVs
and lack of routing efficiency [
17
]. Aadil et al. [
18
] addressed these issues and proposed
a clustering model with energy-aware link-based clustering called EALC. For efficient
clustering, parameters such as energy, degree, cluster formation, and cluster head lifetime
are taken into account. Link quality and transmission range are considered first to reduce
the energy consumption of flying nodes. The K-means density-clustering model used for
high mobility considers distance and energy. This model selects cluster heads (CHs) with
the least computation and maximum throughput and minimizes routing overhead. The
lifetime of UAVs increased with the use of an energy-efficient selection of CHs. A simple
clustering approach is used to reduce computation overhead. Nevertheless, EALC ignored
the communication load, data aggregation, and bandwidth utilization factors.
Arafat and Moh [
19
] proposed an energy-efficient clustering scheme based on particle
swarm optimization for an emergency mission. First, implement swarm-intelligence-based
localization and clustering (SIL and SIC) schemes that define the search space with a
boundary box to reduce computation power. UAVs are placed randomly in the search
space. SIL uses a grouping scheme to calculate the distance between the target UAVs.
The proposed model has an estimation model to measure UAV distance from CH. The
distance between nodes and CH is considered for reducing energy consumption. The
Euclidean distance is utilized for locating UAVs and balancing cluster size. In SIC, cluster
formation and CH selection are performed with a fitness function that considers remaining
energy and distance. The performance metrics used in this paper are energy consumption,
communication load, and delay. Node degree and residual energy are considered to balance
inter-cluster and intra-cluster energy utilization.
Yang et al. [
20
] proposed a probabilistic energy-aware clustering scheme to find the
most efficient path for UAVs using ant colony optimization (ACO). WSN data-gathering
efficiency is achieved with UAVs. The network is divided into clusters, each with a CH,
cluster members (CMs), and UAV. The nodes are stationary with a position-aware CH; the
CH receives information from the UAVs flying around the cluster heads. The proposed
model has three stages. First, a UAV senses data about the farmland event via the ground
segment. Second, the data gathered by UAVs is transmitted to the data center through the
CH. Finally, the data center contains a database and management information system.
To overcome packet loss, long delay, and increased routing overhead, Yu et al. [
21
]
proposed a clustering protocol based on ACO to enhance network performance. A reliable
link supervision method was established due to UAV mobility and topology variation.
The nonlinear processing scheme increases buffer size and link load to control and avoid
congestion on the link. Based on the density of UAVs, two routing strategies are proposed,
namely sparse formation and concentrated formation. ACO-based polymorphism-aware
routing integrates dynamic source routing and ACO.
2.2. UAVs-Based Data Aggregation
In FSNets, the collection and transmission of information through multiple hops
increase energy utilization [
22
]. The data aggregation approach reduces energy utilization
and increases network lifetime by minimizing UAVs load. The data aggregation approaches
reduce the communication cost and energy consumption [
23
]. The researchers developed
aggregation approaches for FSNet without redundant data elimination [24].
Wang et al. [
25
] introduced a UAV-assisted topology-aware data aggregation protocol
in WSN (TA-UAV-DA). The data aggregation approach was inspired by the compressive
sensing approach to reduce the errors rate in the data reconstruction process, extra overhead,
and energy consumption. Balanced tree-based topology construction is performed to

Future Internet 2023,15, 279 4 of 24
minimize the scope and update the matrix measurement. The CMs send data to CH, and
UAV gathers data from the CHs. The simulation results show that the approach performs
better when reconstructing data, and it is more efficient in data aggregation and storage
constraints than a random walk and intelligent compressive sensing.
Wu et al. [
26
] developed an energy-efficient UAV-based data aggregation protocol
(EE-UAV-DA) for WSNs. In EE-UAV-DA scheme, UAVs gather data as data mules. The
proposed method calculates the optimum link for the data mule through all CHs, using a
genetic algorithm that achieves high-energy efficiency. By balancing system throughput,
the proposed approach reduces the delay between the sensors and the sink node. The
optimization scheme provided by heuristic search identifies optimal solutions for joint
CH selection and optimal routes for the data mule to decrease energy consumption. The
objective function calculates and measures each solution’s quality for the optimum path.
Thammawichai [
27
] proposed optimizing communication and computation for multi-
UAV information-gathering applications called OC-mUAV. Multi-hop clustering incorpo-
rates data aggregation by using a mixed-integer optimization formulation with mixed-
integer nonlinear programming. In order to determine the roles of UAVs, the optimal
control problem was formulated. The system framework tries to ensure that the optimal
number of UAVs communicate with BS. To maintain minimum energy consumption during
routing, each UAV acts as an aggregator. An adaptive energy consumption model mini-
mizes energy consumption by considering sensing energy, aggregation energy, transmitting
energy, and receiving multi-UAV energy. To reduce communication and communication
energy, area mapping and target tracking were addressed during testing. Target and sensor
models are used to select the sensor UAV based on a subset of UAVs. The distance between
UAVs is used for mapping. As a result of the data aggregation framework, the network is
flexible and reliable since it is a self-organized network, which prolongs the lifetime of the
network due to multi-hop networks and provides better performance due to clustering of
heterogeneous UAVs.
Dong et al. [
28
] proposed an algorithm to collect and process data in WSN, using
UAVs and mobile agents (MAs) to search for victims at disaster sites. MAs move around
the area to collect data from sensor nodes and share information with UAVs. The UAV
assigns MAs to group leaders. The density of sensor nodes in a group known by the group
leader has high residual energy and is an optimum link to a UAV. MAs’ routing is based on
information-driven static and dynamic mobile agent planning algorithms. The proposed
scheme is efficient in energy and time for any dense network using MAs and UAVs.
To decrease energy utilization in a UAV-aided WSN, Liu and Zhu [
29
] proposed
an energy-efficient data collection method. Sensor nodes are placed randomly in the
environment. The proposed approach uses three transmission modes to solve the short
buffer size of sensor nodes to transmit data within the allotted time slots. The sensor node
selects the modes, i.e., waiting, transmission to a sink node, and uploading to UAV in each
discrete time slot. The sensor node is selected in waiting mode to sleep and not transmit the
status of the node. The sensor node uploads data to the sink node in the second mode. In
the third mode, the sensor node delivers data to the UAV based on the threshold value and
distance condition during the UAV preplanned trajectory visit. The UAV of a fixed-wing
aircraft is deployed at a constant velocity. This article uses a finite-horizon sequential
Markov process and dynamic programming algorithm for the optimized transmission
policy. Secondly, the proposed method optimizes the preplanned trajectory for UAVs using
a recursive random search algorithm.
The authors of [
30
] analyzed the performance of an energy-constrained Internet of
Things (IoT) system that uses a power beacon and UAV for data collection. The study
examined how different system and channel parameters affect outage probability, outage
capacity, and ergodic capacity. In [
31
], the authors explored the challenges and possible
solutions for implementing a fully immersive and interactive industrial metaverse, which is
a virtual space that interacts with the physical world in real time. In the paper, the authors
focused on improving key performance indicators, such as the Age of Information, latency,

Future Internet 2023,15, 279 5 of 24
and reliability through optimizing short-packet structures in 6G URLLC communication.
A cooperative strategy involving an unmanned ground vehicle and UAV is proposed
in [
32
] to collect data from sensor nodes (SNs) in UAV-enabled data collection systems
when SNs may not be able to upload their data because of factors such as insufficient
energy and low flight altitude. A collaborative strategy selection algorithm that combines
multistage-based SN association and UAV-UGV path optimization algorithms was used
to determine trajectories for mobile data collection nodes on the ground and in the air to
minimize mission completion time.
3. Flying Sensor Network Cluster Optimization
In cluster-based flying networks, the selection of CHs and cluster formation requires
special attention to decrease the re-affiliation rate and save FSNet resources [33]. To select
CHs, essential parameters such as the remaining energy, mobility, and flying nodes degree
are considered to obtain optimal clusters [
34
–
36
]. These parameters are optimized to
distribute load among clusters. We use the clustering approach to balance and select CHs
in accordance with [
37
], as shown in Figure 1. Data aggregation is initiated once clusters
are formed.
Future Internet 2023, 15, x FOR PEER REVIEW 6 of 25
Figure 1. Flowchart of proposed system.
Clustering Setup
The HBA is applied in the cluster setup phase to determine the optimal CHs [37]. The
CH selection is based on the HBA to form a balanced cluster. When selecting CHs, the
UAV mobility and neighbor criteria are considered to minimize re-clustering. In FSNet,
once CHs are selected, they broadcast a message containing ID, position, and status. All
UAVs in CH range will receive broadcast messages and join the cluster. Once UAVs join a
cluster, they become CMs and share information with CH. If a UAV receives membership
messages from multiple CH, joining will be based on the distance between the UAV and
CH. If the distance is the same, the random UAVS-CH selection mechanism will take
place. The working of the cluster setup phase is shown in Algorithm 1 below. Once the
cluster is formed, the data-aggregation-and-communication phase is initiated to transmit
the data to the BS.
Algorithm1: Pseudo Code of UAVs Enabled CH Selection.
1 Procedure CH-Selection-Multi-UAVs (MUAVs)()
2 Input: Swarm of UAVs 𝑆𝑊
,
UAV nectar [𝑛], and cluster 𝐶.
3 Output: UAVs-CH
4 call function calculate-UAVs-Nectar (𝑛)
//
v1 represents the number of nodes (UAVs) when there are n total UAVs in the network
5 for 󰇡𝑣=1;𝑣≤ FSNet
C;𝑣++󰇢 do
// selection of UAVs-CH in a random way
6 UAVs-CH[v]=functionRand (𝑆𝑊)
7 end for
8 while (highest-value!=yes) do
Figure 1. Flowchart of proposed system.
As shown in Figure 1, the proposed approach begins with the selection of a CH-UAV.
The selection process determines which UAV will act as the CH. If the node is the CH,
it proceeds to the next step. Then, the CH-UAV broadcasts the time division multiple
access (TDMA) schedules to all member nodes within its cluster. TDMA is a channel
access method that allows multiple nodes to share the same communication channel by
dividing it into different time slots. The CH-UAV receives data from all neighboring nodes
within its cluster. Data aggregation is the process of combining or summarizing data from
multiple sources. The CH-UAV performs data aggregation on the received data, reducing

Future Internet 2023,15, 279 6 of 24
redundancy and improving efficiency. After data aggregation, the CH-UAV sends the
aggregated data to the BS for further processing. If the current node is not CH, it proceeds
to the next step. The non-CH node waits for the TDMA schedule broadcast by the CH-UAV.
This schedule determines when the node can transmit or receive data. The algorithm checks
the energy level of nodes. If the energy is still available, it returns to the CH selection step,
indicating that the next round of the process will begin. When the node’s energy reaches
zero or depletes, the flowchart terminates, and the process ends.
In cluster-based routing for flying sensor networks, CHs may receive multiple copies
of the same dataset from different sensors located in the vicinity. The communication of
data requires more resources as compared to computation. Hence, a method is required to
discard duplicated packets when sending data to the base station at the cluster level. Thus,
network resources such as batteries and bandwidth can be utilized for other purposes. The
network lifetime will increase. Our proposed algorithm works in two phases: cluster setup
and data aggregation.
Clustering Setup
The HBA is applied in the cluster setup phase to determine the optimal CHs [
37
]. The
CH selection is based on the HBA to form a balanced cluster. When selecting CHs, the
UAV mobility and neighbor criteria are considered to minimize re-clustering. In FSNet,
once CHs are selected, they broadcast a message containing ID, position, and status. All
UAVs in CH range will receive broadcast messages and join the cluster. Once UAVs join a
cluster, they become CMs and share information with CH. If a UAV receives membership
messages from multiple CH, joining will be based on the distance between the UAV and
CH. If the distance is the same, the random UAVS-CH selection mechanism will take place.
The working of the cluster setup phase is shown in Algorithm 1 below. Once the cluster is
formed, the data-aggregation-and-communication phase is initiated to transmit the data to
the BS.
Algorithm 1: Pseudo Code of UAVs Enabled CH Selection.
1 Procedure CH-Selection-Multi-UAVs (MUAVs)()
2 Input : Swarm of UAVs SWUAV, UAV nectar [nU AV ], and cluster CF SNet.
3 Output: UAVs-CH
4call function calculate-UAVs-Nectar (nUAV)
// v1 represents the number of nodes (UAVs) when there are ntotal UAVs in the network
5for(v=1; v≤CFSNet;v+ +)do
// selection of UAVs-CH in a random way
6 UAVs-CH[v]=functionRand (SWU AV )
7 end for
8 while (highest-value! = yes) do
9for(v1=1; v1≤nUAV;v1=v1+1)do
// the suitability of current selection is computed
10 if (v1 in UAVs-CH) then
11 Fitness Value FValueU AV =FValueU AV +1(SWU AV [u]+AFVUAV )
// Average fitness value AFVUAV
12 end if
13 end for
14 if (FValueU AV <PFVal ueU AV ) then
//PFVal ueU AV is the suitable value in the existing solution
15 swap FValueU AV
16 end if
17 if (UAVs-CH-optimum! = yes) then
18
while(empb! =0)do // Employed bee (empb)
// visiting of bees employed till empty, where αij is UAV affiliation with the current
round while yis the neighborhood size
19 UAVj(x+1)=U AVj(x)+αi j ∗y
// selection of different UAVs from fellow citizen

Future Internet 2023,15, 279 7 of 24
Algorithm 1: Cont.
20 end while
21 Pri=WUAVi
∑k
j=1WUAVj
// the new UAVs probability Priwill be calculated based on Weight of UAV (WUAV )
22 while (the Obees 6=Є) do //Onlooker bees (Obees)
23 Selection of another set of UAVs-CH will be carried out subject to the probability Pri
24 end while
25 Else
26 return UAVs-CH
27 end while
28 end procedure
4. Data Aggregation and Communication
We collect data from flying UAVs and match the data to discard similar data sent by
multiple sensors in the data aggregation process. Data aggregation is divided into two
levels. In level 1, the data are collected using a TDMA schedule when multiple sensors
simultaneously communicate data.
A near-linear time algorithm is proposed in this paper for the data aggregation level 2
problem in FSNet. The data coming from sensors is converted into a long string. According
to our knowledge, this is the leading work to assume nontrivial alignment among the
strings and the patterns. Specifically, we demonstrate the data aggregation problem in two
ways: First, to sanction approximating
D[i]
’s, and second, an additional procedure sanction
named partial data move, for the movement of partial data from one position to another in
a data.
This similarity among the
X
and
Y
data is known as data match with moves (DMM)
and designated as
d(X,Y)
[
38
]. DMM is a powerful data-matching tool that can greatly
benefit FSNet data aggregation. By using DMM, network operators can easily match
data from different sources, allowing for a more accurate and comprehensive analysis of
the data. The DMM algorithm can take advantage of UAV mobility by assigning them
to different regions and optimizing their movement patterns to efficiently collect data.
Moreover, DMM can provide a wide range of benefits, including reducing the amount of
data, reducing bandwidth usage, increasing energy efficiency, and supporting proximity-
based data aggregation. There are various applications in computational biology where
partial data matches are considered a primeval in multiple situations. Moving a larger
subsequence is similar to the insert or delete operation; during text processing, moving a
large array together might be assumed, like reordering to deleting or inserting typescripts.
Keep in mind that the nontrivial placements are still a challenge for DMM. Hence,
d(X,Y)
is the size of the small structure of edit procedures that convert
Y
to
X
; the allowable
procedure affects the data stated. The deletion of a character at location,
loc
, transforms
X
to X[1]. . . X[loc −1],X[loc +1]. . . X[n].
•
The insertion of a character, “
c
” at a location, “
loc
”, gives
X[1]. . . X[loc −1]
,
c
,
X[loc]. . . X[n].
•
The substitution of a character at the location, “
loc
”, with character, ”
c
”, results in
X[1]. . . X[loc −1],c,X[loc +1]. . . X[n].
•
The partial data movement with factors 1
≤loc ≤loc2≤k≤n
converts
X[1]. . . X[n]
into X[1]. . . X[loc −1],X[loc2]. . . X[loc3−1],X[loc]. . . X[loc2−1],X[loc3]. . . X[n].
The data are identical when the edit distance between two data is “0”. The metric
represents its measure. The transformation is performed in several operations, and each
operation’s cost is equal even in the inverse case. Hence,
d(X,Y)=d(Y,X)
; then, every
distance resulting from transforming one datum to another must follow the triangular
inequity. The restrictions of the interaction of edit operations are none. These restrictions
may be as follows: it is relatively conceivable for a fractional data move to take a fractional

Future Internet 2023,15, 279 8 of 24
datum to a different position and then for a successive data move to function on a fractional
datum that overlays the relocated fractional datum and its neighboring typescripts.
The deterministic algorithm results in the DMM problem, and the running time
complexity is
O(nlogn)
. An algorithm returns the equivalent array,
“Ar”
, where every
Ar[loc]
is estimated to be close to the
O(lognlog∗n)
factor. The proposed methodology
depends on inserting data to a vector of arrays below
L
1 metric. The
L
1 size among these
arrays is O(lognlog∗n), the estimate of the DMM between the two original data.
The proposed method can further solve several problems beyond the primary data
aggregation Level 2 problem. These contain data-similarity search problems. A study
presented in [
39
] showed that calculating the distance among two datasets is NP-Complete.
An approximation algorithm with complexity
O(logn)
was presented to find the distance
among datasets. However, the approximation may not resolve the data-match problem.
The proposed scheme focuses on the vital components. Firstly, we parsed data into a
hierarchy of partial data. We use a simple hierarchical mechanism for parsing called edit-
sensitive parsing (ESP), which generates a tree with three degrees [
40
]. ESP may not be an
innovative parsing method; however, it is an effort to make straightforward the procedural
details of relating predefined coin throwing to obtain classified data fragmentation. It is
expected that the ease of ESP assists in/exposes more uses of classified data decays. The
next module of this research is the approximate distance preservative data inserting to
array spaces based on hierarchical parsing.
4.1. Data Embedding
We demonstrate a data-embedding scheme, which embeds data into a multidimen-
sional matrix. Assume some data,
X
, over an alphabet,
∑
. The data,
X
, will be embedded
as
Em(X)
, an array with multi-magnitudes,
O(|∑||X|)
, but the number of magnitudes of
the nonzero array will be relatively minimum, indeed O(|X|).
The time complexity of the embedding
Em
process is linear. The proposed scheme will
parse Xinto different fractional data and reflect the multi-set
T(X)
of these fractional data.
We confirm that the size of
T(X)
is as a maximum
2|X|
. Hence,
Em(X)
is the distinguishing
array for
T(X)
. The process through which the parse tree
T(X)
will generate is known as
ESP. The following subsection explores the ESP.
4.1.1. EPS
The parse tree,
EST(X)
, that is formed for data
X
:
X
is the breakdown structure of par-
tial data analogous to the nodes of
EST(X)
. The aim is to limit the data-editing operations.
A clear EST contains all dynamic data of length 2
loc
, namely
Xhloc22loc . . . (loc2+1)2loc −1i ∈loc
and
loc2
; it results in a complete binary tree. How-
ever, if
X
is updated using addition or removal to obtain
X0
,
X
and
X0
will be construed
using the same technique to two dissimilar hierarchical partial datasets; thus, the resultant
embedding will not preserve approximation.
Suppose we have data
X
; the next step is to form an ESP tree in a hierarchal fashion
with
Pi(X)
repetitions. Every repetition produces a different level of EST. At every repe-
tition,
i
, the process initiates with data,
Xi
, and divides them into chunks of size two or
three. We substitute every chunk analogous to
X[loc3. . . loc2]
by name and refer to the pair
(loc,h(X[loc3. . . loc2])). Moreover, hcorresponds to a 1-1 hash function on partial data X.
Suppose
X
0
=X
, and the repetitions until the length of data left become 1. The EST
tree of
X
contains levels, and for every string of
Xloc −
1, a node at level
i
must exist, and
the children are the nodes in level
loc −
1. Here, a leaf node is each data unit of
X
0
=X
.
More precisely, we can make the partitions of
Si
data into dissimilar non-overlapping units.
The data can be divided into non-overlapping units in three ways:
(a)
Maximum adjacent partial data of
Xi
that comprise a repetitive sign (
X
0 shows in the
form alfor a∈Σiwhere l>1).
(b)
Length of partial data (Long) at least log∗|∑l oc −1|not of type 1 above.
(c)
Length of partial data (short) less than log∗|∑l oc −1|not of type 1.

Future Internet 2023,15, 279 9 of 24
The general term “meta block” (mb) is used for all such partial data. To produce
next-level parsing, we process each mb as demonstrated in the following subsections.
4.1.2. Type 2: Long Data without Duplications
We assume a dataset where two consecutive symbols are duplicates and represent an
mb of type 2. Assuming a structure, X, without duplications (i.e., X[loc]6=X[loc +1]for
loc =
1
. . . |X|−
1), we select as a maximum
|X|/
2 and minimum
|X|/
3 partial data of
X
as
a node. We obtain
X
upon concatenating these nodes. The first phase comprises repeating
the reduction process of an alphabet.
Reduction of alphabet (
∑
): For every character
C[loc]
, calculate a new tag.
C[loc −1]
is the symbol located to the left of
C[loc]
, and assume
C[loc]
and
C[loc −1]
are denoted as
binary numbers. The least-significant bit (LSB) key where
C[loc]
differs from
C[loc −1]
is
represented by
Le
, and assume bit (
Le
,
C[i]
) is the value of
C[i]
at the
Leth
bit position. For
example, the location of bit
Le
is next to the character at the former index, i.e., form label
(C[loc]) as Le +bit(Le,C[loc]).
Lemma 1. For some loc, if C[loc]6=C[l oc +1], then C[loc]6=label(C[loc +1]).
Proof.
Supposing the LSB location, where
C[loc]
differs from
C[loc +1]
, is similar in a way
where
C[loc]
also differs from
C[loc −1]
(else,
labelC[loc]6=label(C[loc +1])
). However,
the bit character at this position in every symbol must be different; therefore,
labelC[loc]6=
label(C[l oc +1]).
Adopting this method, we create an innovative series. If the existing alphabets have
length,
ï
, then the extracted alphabets have size, 2
log|η|
. We currently repeat (repetition
is orthogonal to the duplication that produces an EST tree of
X
; repeating on
C
that is a
subseries with no matching contiguous characters) and make the character decrease until
the length of the alphabet is unable to shrink. This will take
log∗|η|
repetitions. Note that
the labels for the first log∗|η|symbols will not exist.
The lemma states that if a symbol at position
C[loc]
is not equal to the symbol at
position
C[loc +1]
, then the label assigned to
C[loc]
is not equal to the label assigned to
C[loc +1]
. Lemma 1’s goal is to establish a connection between symbols and their corre-
sponding labels based on how they differ from one another. Lemma 1’s proof demonstrates
that if there is a difference between two symbols, (
C[loc]
and
C[loc +1]
), their labels will
also be different. The subsequent actions and procedures in the text are theoretically
justified by this lemma. 
Lemma 2. After the last reiteration of the ∑reduction, the size of ∑is 6.ï.
Proof.
Upon every repetition of cataloguing, the size of the alphabet is reduced from
|∑|
to 2
[log|∑|]
. If
|∑|>
6, then 2
[log|∑|]
is firmly smaller than 6. Ahas no duplicate symbols
contiguously, nor do the final order of tags on Aby Lemma 1 iteratively.
Lemma 2 plays a crucial role in establishing the size of the alphabet
(∑)
after the
last iteration of cataloguing in the given text. It states that the size of
∑
is 6 times the
original alphabet size (
ï
) after the last repetition of cataloguing. The proof of Lemma 2
demonstrates that if the initial alphabet size is greater than 6, then the reduction process
reduces the alphabet size to a value that is strictly smaller than 6.
Lastly, three passes over the order of labels were accomplished to decrease the alphabet
from {0, 1, 2}: initially, we substitute every 3 with the minimum item from {0, 1, 2} that is
not in the neighborhood of 3, and then we perform the same operation for every 4 and 5.
This produces a series of symbols extracted from the
∑{0, 1, 2}
, where no contiguous labels
are equal. We designate this series A0.
We currently choose distinct positions, known as landmarks, from the structures that
are closely related to each other. We initially chose some location, I, and a local maximum
as a landmark, such as A0[loc −1]<A0[loc]>A0[loc +1].

Future Internet 2023,15, 279 10 of 24
Two local maximums might have four overriding symbols. Moreover, we chose some
ias a landmark, i.e., local minima, such as
A0[loc −1]<A0[loc]<A0[loc +1]
, that was not
contiguous to a previously selected landmark. In Figures 2and 3, the process is depicted
graphically.
Future Internet 2023, 15, x FOR PEER REVIEW 10 of 25
The lemma states that if a symbol at position 𝐶[𝑙𝑜𝑐] is not equal to the symbol at
position 𝐶[𝑙𝑜𝑐 + 1], then the label assigned to 𝐶[𝑙𝑜𝑐] is not equal to the label assigned to
𝐶[𝑙𝑜𝑐 + 1]. Lemma 1’s goal is to establish a connection between symbols and their corre-
sponding labels based on how they differ from one another. Lemma 1’s proof demon-
strates that if there is a difference between two symbols, (𝐶[𝑙𝑜𝑐] and 𝐶[𝑙𝑜𝑐+1] ), their
labels will also be different. The subsequent actions and procedures in the text are theo-
retically justified by this lemma. ∎
Lemma 2. After the last reiteration of the ∑ reduction, the size of ∑ is 6.ɳ.
Proof. Upon every repetition of cataloguing, the size of the alphabet is reduced from |∑|
to 2[𝑙𝑜𝑔|∑|]. If |∑|>6, then 2[𝑙𝑜𝑔|∑|] is firmly smaller than 6. A has no duplicate sym-
bols contiguously, nor do the final order of tags on A by Lemma 1 iteratively.
Lemma 2 plays a crucial role in establishing the size of the alphabet (∑) after the last
iteration of cataloguing in the given text. It states that the size of ∑ is 6 times the original
alphabet size (ɳ) after the last repetition of cataloguing. The proof of Lemma 2 demon-
strates that if the initial alphabet size is greater than 6, then the reduction process reduces
the alphabet size to a value that is strictly smaller than 6.
Lastly, three passes over the order of labels were accomplished to decrease the alpha-
bet from {0, 1, 2}: initially, we substitute every 3 with the minimum item from {0, 1, 2} that
is not in the neighborhood of 3, and then we perform the same operation for every 4 and
5. This produces a series of symbols extracted from the ∑󰇝0,1,2󰇞, where no contiguous
labels are equal. We designate this series 𝐴󰆒.
We currently choose distinct positions, known as landmarks, from the structures that
are closely related to each other. We initially chose some location, I, and a local maximum
as a landmark, such as 𝐴󰆒[𝑙𝑜𝑐 − 1] < 𝐴󰆒[𝑙𝑜𝑐] > 𝐴󰆒[𝑙𝑜𝑐 + 1]. ∎
Two local maximums might have four overriding symbols. Moreover, we chose some
i as a landmark, i.e., local minima, such as 𝐴󰆒[𝑙𝑜𝑐 − 1] < 𝐴󰆒[𝑙𝑜𝑐] < 𝐴󰆒[𝑙𝑜𝑐 + 1],that was not
contiguous to a previously selected landmark. In Figures 2 and 3, the process is depicted
graphically.
Figure 2. Landmark finding and alphabet reduction process.
Figure 3. Nodes’ formation based on landmark symbols.
Lemma 3. For some two consecutive landmark locations, 𝑙𝑜𝑐 and 𝑙𝑜𝑐,2≤|𝑙𝑜𝑐 − 𝑙𝑜𝑐|≤3.
Proof: Using our tagging mechanism, we claim that no contiguous pair of symbols is
tagged—subsequently, we may not have two contiguous local maximums and specifically
inhibit tagging local minima next to a local minimum. A modest case investigation demon-
strates that the parting of landmark locations is two overriding labels. ∎
Figure 2. Landmark finding and alphabet reduction process.
Future Internet 2023, 15, x FOR PEER REVIEW 10 of 25
The lemma states that if a symbol at position 𝐶[𝑙𝑜𝑐] is not equal to the symbol at
position 𝐶[𝑙𝑜𝑐 + 1], then the label assigned to 𝐶[𝑙𝑜𝑐] is not equal to the label assigned to
𝐶[𝑙𝑜𝑐 + 1]. Lemma 1’s goal is to establish a connection between symbols and their corre-
sponding labels based on how they differ from one another. Lemma 1’s proof demon-
strates that if there is a difference between two symbols, (𝐶[𝑙𝑜𝑐] and 𝐶[𝑙𝑜𝑐 + 1] ), their
labels will also be different. The subsequent actions and procedures in the text are theo-
retically justified by this lemma. ∎
Lemma 2. After the last reiteration of the ∑ reduction, the size of ∑ is 6.ɳ.
Proof. Upon every repetition of cataloguing, the size of the alphabet is reduced from |∑|
to 2[𝑙𝑜𝑔|∑|]. If |∑|>6, then 2[𝑙𝑜𝑔|∑|] is firmly smaller than 6. A has no duplicate sym-
bols contiguously, nor do the final order of tags on A by Lemma 1 iteratively.
Lemma 2 plays a crucial role in establishing the size of the alphabet (∑) after the last
iteration of cataloguing in the given text. It states that the size of ∑ is 6 times the original
alphabet size (ɳ) after the last repetition of cataloguing. The proof of Lemma 2 demon-
strates that if the initial alphabet size is greater than 6, then the reduction process reduces
the alphabet size to a value that is strictly smaller than 6.
Lastly, three passes over the order of labels were accomplished to decrease the alpha-
bet from {0, 1, 2}: initially, we substitute every 3 with the minimum item from {0, 1, 2} that
is not in the neighborhood of 3, and then we perform the same operation for every 4 and
5. This produces a series of symbols extracted from the ∑󰇝0,1,2󰇞, where no contiguous
labels are equal. We designate this series 𝐴󰆒.
We currently choose distinct positions, known as landmarks, from the structures that
are closely related to each other. We initially chose some location, I, and a local maximum
as a landmark, such as 𝐴󰆒[𝑙𝑜𝑐 − 1] < 𝐴󰆒[𝑙𝑜𝑐] > 𝐴󰆒[𝑙𝑜𝑐 + 1]. ∎
Two local maximums might have four overriding symbols. Moreover, we chose some
i as a landmark, i.e., local minima, such as 𝐴󰆒[𝑙𝑜𝑐 − 1] < 𝐴󰆒[𝑙𝑜𝑐] < 𝐴󰆒[𝑙𝑜𝑐 + 1],that was not
contiguous to a previously selected landmark. In Figures 2 and 3, the process is depicted
graphically.
Figure 2. Landmark finding and alphabet reduction process.
Figure 3. Nodes’ formation based on landmark symbols.
Lemma 3. For some two consecutive landmark locations, 𝑙𝑜𝑐 and 𝑙𝑜𝑐,2≤|𝑙𝑜𝑐 − 𝑙𝑜𝑐|≤3.
Proof: Using our tagging mechanism, we claim that no contiguous pair of symbols is
tagged—subsequently, we may not have two contiguous local maximums and specifically
inhibit tagging local minima next to a local minimum. A modest case investigation demon-
strates that the parting of landmark locations is two overriding labels. ∎
Figure 3. Nodes’ formation based on landmark symbols.
Lemma 3. For some two consecutive landmark locations, l oc and loc2, 2 ≤|loc −loc2|≤3.
Proof.
Using our tagging mechanism, we claim that no contiguous pair of symbols is
tagged—subsequently, we may not have two contiguous local maximums and specifi-
cally inhibit tagging local minima next to a local minimum. A modest case investigation
demonstrates that the parting of landmark locations is two overriding labels. 
Lemma 4.
Defining the nearby landmark to location,
loc
, subject to only 5 adjacent locations to the
right and log∗|η|+5to the left.
Proof.
Once a reiteration of alphabet reduction is performed, every symbol depends merely
on its left label. We iterate this
log∗|η|
time; therefore, the symbol at a location,
i
, is based on
log∗|η|
for the left labels. As soon as we accomplish the last step of reducing the
∑
form
∑
of six (6) to
∑
of three (3), the last label at a location,
i
, is based on a max of three extra labels
to its right and left. We must tag every local maximum location and, formerly, every local
minimum position not contiguous to a local maximum; therefore, we must inspect max
two symbols to the right of iand two labels to the left, which, in order, depends on three
labels to the right and
log∗|η|+
3 labels to the left. The aggregate dependence is, hence,
as indicated. We currently demonstrate how to divide Ainto units of size 3 or 2 nearby
landmarks. 
4.1.3. Type 1 (Repeating mbs) and Type 3 (Short mbs)
We look for landmarks discovered without any difficulty in the local neighborhood.
Hence, we assume data blocks containing a distinct repetitive symbol as big landmarks.
Type 3 and Type 1 blocks are parsed in a usual way; the details are given for completeness.
The mbs having size one are attached to the left or the right of the repeating mb. The
attachment will preferably be to the left if both are possible. The mbs of size two or
three are remembered as blocks without further splitting, whereas an mb of length four is
allocated into two blocks of size two. In each mb with a size of five or greater, the parsing
may be carried out on the leftmost three labels as a block, and then reiterate the rest.
4.1.4. Constructing ET (X)
While partitioning
Xloc
into 2 or 3 labels,
Xloc +
1 is constructed by substituting every
block,
bl
, by
h f (bl)
, where
h f
is a 1-1 naming hash function. It is essential to mention that

Future Internet 2023,15, 279 11 of 24
the units of distinct levels will call hash functions onto distinct domains to compute names.
To this point, the focus is on any given level
i
. Using the random property, the computation
of
h f ()
for a specific unit of size 2 or 3 will take
O(1)
time. This produces the series
Xloc +
1;
this process is reiterated till the series is of size one or till the tree root. Let
Pi(X)
represent
total nodes at level iin
ET(X)
. The original data,
M0(X)=|X|
, are used to design the
first (leaf) level from the symbols. We have
Pi(X)/
3
≤Pi+1(X)≤[Pi(X)/2]
. Hence,
3
2|X|≤Pi|Xi|≤
2
|X|
. Therefore, for every
i
,
|∑i|≤|X|
and, thus,
log∗|∑i|≤log∗|X|
are
shown in Figure 4.
Future Internet 2023, 15, x FOR PEER REVIEW 11 of 25
Lemma 4. Defining the nearby landmark to location, 𝑙𝑜𝑐, subject to only 5 adjacent locations to
the right and 𝑙𝑜𝑔∗|𝜂|+5 to the left.
Proof: Once a reiteration of alphabet reduction is performed, every symbol depends
merely on its left label. We iterate this 𝑙𝑜𝑔∗|𝜂| time; therefore, the symbol at a location, 𝑖,
is based on 𝑙𝑜𝑔∗|𝜂| for the left labels. As soon as we accomplish the last step of reducing
the ∑ form ∑ of six (6) to ∑ of three (3), the last label at a location, 𝑖, is based on a max
of three extra labels to its right and left. We must tag every local maximum location and,
formerly, every local minimum position not contiguous to a local maximum; therefore,
we must inspect max two symbols to the right of i and two labels to the left, which, in
order, depends on three labels to the right and 𝑙𝑜𝑔∗|𝜂|+3 labels to the left. The aggregate
dependence is, hence, as indicated. We currently demonstrate how to divide A into units
of size 3 or 2 nearby landmarks. ∎
4.1.3. Type 1 (Repeating mbs) and Type 3 (Short mbs)
We look for landmarks discovered without any difficulty in the local neighborhood.
Hence, we assume data blocks containing a distinct repetitive symbol as big landmarks.
Type 3 and Type 1 blocks are parsed in a usual way; the details are given for completeness.
The mbs having size one are aached to the left or the right of the repeating mb. The
aachment will preferably be to the left if both are possible. The mbs of size two or three
are remembered as blocks without further spliing, whereas an mb of length four is allo-
cated into two blocks of size two. In each mb with a size of five or greater, the parsing may
be carried out on the leftmost three labels as a block, and then reiterate the rest.
4.1.4. Constructing ET (X)
While partitioning 𝑋𝑙𝑜𝑐 into 2 or 3 labels, 𝑋𝑙𝑜𝑐 + 1 is constructed by substituting
every block, 𝑏𝑙, by ℎ𝑓(𝑏𝑙), where ℎ𝑓 is a 1-1 naming hash function. It is essential to men-
tion that the units of distinct levels will call hash functions onto distinct domains to com-
pute names. To this point, the focus is on any given level 𝑖. Using the random property,
the computation of ℎ𝑓() for a specific unit of size 2 or 3 will take 𝑂(1) time. This pro-
duces the series 𝑋𝑙𝑜𝑐 + 1; this process is reiterated till the series is of size one or till the
tree root. Let 𝑃(𝑋) represent total nodes at level i in 𝐸𝑇(𝑋). The original data, 𝑀(𝑋) =
|𝑋|, are used to design the first (leaf) level from the symbols. We have 𝑃(𝑋)/3 ≤ 𝑃(𝑋) ≤
[𝑃(𝑋)/2] . Hence, 
|𝑋|≤𝑃
|𝑋|≤2
|𝑋| . Therefore, for every 𝑖 , |∑| ≤ |𝑋| and, thus,
𝑙𝑜𝑔∗|∑| ≤ 𝑙𝑜𝑔∗|𝑋| are shown in Figure 4.
Figure 4. Representation of node structure hierarchically in parse tree based on string S.
Theorem 1. Given the data, 𝑋, the 𝐸𝑇(𝑋) can be calculated in 𝑂(|𝑋| 𝑙𝑜𝑔∗|𝑋|) time.
Figure 4. Representation of node structure hierarchically in parse tree based on string S.
Theorem 1. Given the data, X, the ET(X)can be calculated in O(|X|log∗|X|)time.
4.1.5. Properties of ESP
How to calculate the
ET(X)
for some data
X
is defined above. Every node nin
ET(X)
denotes the partial data of
X
obtained from the leaf nodes on the merging in the subtree at
the root node n.
Definition 1.
Describe the multi-set
T(X)
such that all partial data of
X
are designated by the
nodes of
ET(X)
(for each level). The characteristic array
A(X)
of
T(X)
, i.e.,
A(X)|n|
, can be
defined as the sum of occurrences a partial data
n
appears in
T(X)
. In conclusion,
Ai(X)
the
features array limited to those nodes appear at a level i in ET(X).
T(X)
contains as a maximum 2
|X|
data having size
|X|
An (X) is
O(|∑|+|X|)
dimen-
sional array as its dominion is some data that exist in T(X).
The typical
L1
distance between two arrays
a1
&
a2
by
||a1−a2||
1 is specified.
|A(X)−A(Y)|
1
=PX∈T(X)∪T(Y)|A(X)[x]−A(Y)[x]|
. Recall that
d(X,Y)
indicates the
match with moves among data Yand X.
Theorem 2.
For data
Y
&
X
, suppose
n
be maximum
(|Y|,|X|)
. Then
|A(Y)−A(X)|
1
=
O(lognlog∗n)d(X,Y).
4.2. Upper Bound Proof |A(Y)−A(X)|1=O(lognlog∗n)d(X,Y)
Proof.
Express this bound on
L
1 space, assume the impact of the edit procedures, and
show that all adds a role to the L1 distance limited by O(lognlog∗n). Editing processes are
permitted to overlay on blocks. We present a Lemma applicable to all data, except with no
contiguous repetitive alphabets. 
Lemma 5.
The nearby landmark to any character of
Xloc
is computed by at most five successive
characters of Xloc to the right and at most log∗|Σloc|+5repeated characters of Xito the left.

Future Internet 2023,15, 279 12 of 24
Proof.
Assume that a character of
Xloc
, i.e.,
Xloc [loc2]
, indicates the mechanism to identify
the nearby landmark.
Type 1 Iterating mb: A lengthy duplication of a character,
c
, is considered a distinct
and larger landmark.
Xloc [loc2]
is contained within such an mb if
Xloc [loc2]=Xl oc [loc2+1]
or if
Xloc [loc2]=Xl oc [loc2−1]
. We also assume
Xloc [loc2]
to be part of a reiterating partial
data if
Xloc [loc2−1]=Xl oc [loc2−2]
;
Xloc [loc2+1]=Xl oc [loc2+2]
; and
Xloc [loc2]
6
=
Xloc [loc2+1]and Xl oc [loc2]6=Xloc[loc2−1].
Type 2 and type 3 Nonrepeating mbs: When
Xloc [loc2]
is not a character in re-counting
mb, formerly choose it either in a long or short mb. We investigate the partial data
Xloc [loc2−log∗|Σl oc |−3 . . . loc2−1]
. When there is a
k
such that
Xloc [loc3]=Xl oc [loc3−1]
and
loc3
is more significant than all, a repeating mb ending at location
loc3
exists. In the
landmark, thus, we analyze
Xloc [loc2]
as a short mb part, beginning at
X[loc3+1]
. In-
specting the partial data
X[loc2+1 . . . loc2+5]
permits us to find if there is an additional
repeating mb nearby location,
loc2
, and we can decide the formation of a node comprising
Xloc [loc2]
. When no repeating mb is marked in
Xloc [loc2−log∗|Σl oc |−3 . . . loc2−1]
, it is
possible to use the alphabet decrease procedure to find a landmark. The ability to find a
nearby landmark to a character through observing only a limited number of successive
nearby codes demonstrates that if a modification occurs outside this area, a similar land-
mark will be found; hence, a similar node will be shaped comprising that symbol. This
permits the verification of the subsequent lemma. 
Lemma 6.
Inserting
loc3≤log∗n+
10 contiguous symbols into
X
to obtain
X0
means
|Ai(X)−Ai(X0)|1≤2(log∗n+10)Єlevels.
Proof.
We have a contribution after the insertion itself into the
L
1 distance and its effect on
the nearby vicinity. Assume that the aggregate of characters at the level
i
break down to
distinct nodes next to addition equated to earlier nodes. Consider the total characters at
a level
i
break down in a different way as a result of the insertion
Pi
. Lemma 4.5 proves
that in a non-overlapping mb, any character
log∗|Σloc|+
5 indexes to the right or above five
indexes to the left of each character can be altered and will identify the identical nearby
landmark; hence, it will be shaped according to similar nodes. Hence, it will not pay for
Pi
.
In the same way, for an overlapping mb, any character within the block will be parsed into
a similar node (i.e., into a tripartite of that character), excluding the last four characters and
depending on the block size.
Thus, for an overriding mb,
Pi≤
4. The total characters that are lower-level parsed in
a different way into nodes as a result of the insertion are max
Pi−1
2
, and there is an area
of 5 characters at maximum to the left, plus
log∗|Σi|+
5 characters on the right side are
parsed differently at a level
i
. As noted earlier,
|Σi|≤|X|≤n
, and the recurrence
Pi≤Pi−
1
2+log∗n+
10 can consequently form. If
Pi−
1
≤
2
(log∗n+10)
, then
Pi≤
2
(log∗n+10)
.
Insertion point,
P0≤log∗n+
10. To conclude,
|Ai(X)−Ai(X0)|
1
≤
2
Pi−1
2
, so then we
might miss Pi−1
2ancient nodes and obtain these various new nodes. 
Lemma 7.
Removing
k<log∗n+
10 contiguous characters from
X
to obtain
X0
means
|Ai(X)−Ai(X0)|1≤2(log∗n+10).
Proof.
Notice that the removal of a series of symbols is exactly the double to addition of that
series at the similar index. Assume that a series of symbols pop in and then are removed;
the resulting data are the same as the original data. Hence, the modified nodes number
must be essentially limited by its equal quantity to the insert, as proved in Lemma 6. We
merge both lemmas to confirm that modifying processes limited the parse-tree influences.

Lemma 8.
When a particular allowed operation of edit distance alters data
X
to
X0
, then
|A(X)−A(X0)|1≤8logn(log∗n+10).

Future Internet 2023,15, 279 13 of 24
Proof. Each permissible procedure is assumed.
Character edit processes
The scenario for inserting follows straightaway from Lemma 6, as the character inser-
tion operation will influence the breakdown of max 2
(log∗n+10)
characters at all levels
and the maximum levels
log2n
. Overall,
|A(X)−A(X0)|
1
≤
2
logn(log∗n+10)
. Likewise,
the scenario for deletion follows instantaneously from Lemma 7. To conclude, the case for
substitution is presented by noticing that a symbol substitution assumed that can be used
for removing instantly contiguous to an addition.
Partial data Moves
If the size of partial data being moved is
log∗n+
10 at maximum, then a move can
be said to be a deletion of the partial data following its reinsertion somewhere else. From
Lemma 6 and Lemma 7, we see that
|A(X)−A(X0)|
1
≤
4
logn(log∗n+10)
. Otherwise, we
assume parsing of partial data by ESP. Assume a symbol in a non-iterating mb greater than
log∗+
5 symbols from the beginning of partial data and greater than 5 symbols from the tail.
As per Lemma 5, only symbols inside the partial data being moved decide how that symbol
is parsed. Therefore, the parsing of these symbols and, hence, the contribution to
A(X)
are
free of the position of partial data in original data. Only the
log∗n+
5 symbols at the start
and 5 symbols of the partial data at the end will influence the data-parsing procedure. We
can consider these to be the deletion of two partial data of the size
k≤log∗n+
10 and their
reinsertion somewhere else.
Lemma 8 demonstrates that each permissible action influences the
L
1 conversion
distance by 8
logn(log∗n+10)
maximum. Assume we initiate with
Y
and accomplish a
sequence of
d
editing processes, generating
Y1
,
Y
2,
. . . Yd
as a result. To conclude,
Yd=X
,
so
|A(Yd)−A(X)|
1
=
0. We start with a number,
|A(Y)−A(X)|
1; in addition, we are
aware that

AYloc2−AYloc2+1
≤
8
logn(log∗n+10)
was discussed above. Henceforth,
as
d(X,Y)
steps, convert
Y
to
X
, and then
|A(Y)−A(X)|1
8logn(log∗n+10)≤d(X,Y)
,
giving around d(X,Y).8logn(log∗n+10).
4.3. Data Aggregation Level 2 Problem Solution
In this subsection, an algorithm is proposed that solves the problem of DMM. For
any data
X
, we adopt that
A(X)
needs to be placed in the space of
O(|X|)
via registering
nonzero parts only of
|X|
. Furthermore, appropriately, we save
A(X)[x]
as an array indexed
by h(x)if it is nonzero, and we hold xas a reference to X, along with |x|.
The following outcome on pairwise data association is tracked directly from Theorems
1 and 2 composed with the surveillance that is given:
A(Y)
and
A(X)|A(Y)−A(X)|
1
found in O(|Y|+|X|)time.
Theorem 3.
Given data
X
and
Y
with
n=max(|X|,|Y|)
, to approximate a deterministic
algorithm used for
d(X,Y)
to precise up to an
O(lognlog∗n)
factor in
O(nlog∗n)
time with
O(n)space.
4.3.1. Pruning Lemma
Before solving the data-match problem, pattern p of size m associate with
t[loc . . . n]
for each
i
, then there will be
O(n)
comparisons. Moreover, we have to calculate the distance
among
p
and
t[loc . . . loc3]
for all possible
loc3≥loc
to calculate the optimal placement
beginning at the location
i
, that shows sub-problems generally
O(mn)
. In the worst case,
the algorithm of classical dynamic programming accomplishes the whole evaluations in
O(mn)
time at max by using the dependency between sub-problems. In the algorithm, a
different methodology is proposed. Initially, the below crucial observations were made:
Lemma 9.
(Pruning Lemma) Given an arrangement, t, and string,
s
,
∀loc
,
loc2
: 1
≤loc ≤
loc2≤n,d(t,s[loc . . . loc +m−1]≤2d(t,s[loc . . . loc2]) .

Future Internet 2023,15, 279 14 of 24
Proof.
Note that for all
j
values in lemma,
d(t,s[loc . . . loc2]) ≥|(Y−loc +1)−m|
, as these
multiple symbols must be deleted or inserted. By triangle inequality of match with moves,
for all, loc2d(t,s[loc . . . loc +m−1].
≤d(t,s[loc . . . loc2]) +d(s[loc . . . loc2],s[loc . . . loc +m−1]
=d(t,s[loc . . . loc2]) +|(Y−loc +1)−m|
≤2d(t,s[loc . . . loc2])
The lengthiest common prefix followed to assume
s[loc . . . loc2]
and
s[loc . . . loc +m−1]
.
The above Lemma importance is that it serves to estimate only
O(n)
distances, such
as
d(t,s loc . . . loc +m−1)
for all
i
values, to solve the data-match problem DMM, equal to
a factor 2 approximation. Therefore, it trims away candidates from the “quadratic” number
of distance calculations that an honest process would require. 
4.3.2. ESP Sub-Trees
We estimate distance among partial data s and the pattern t by matching the parsing
ESP of two patterns. On the other hand, it would be costly and useless to parse the partial
data s. In this subsection, we indicate that an ESP tree is assigned to a datum, and being
inspired by a partial datum means that the subtree will have similar editing sensitivity
features as the complete one.
Definition 2.
Let
ETloc (X)lo c2
at
loc2
, such that loc represents the level of UAV in the breakdown
of X.
The set of values
X[a1. . . an]
to the tags on last level of the sub-tree, where (root)
ETloc (X)lo c2
is defined as range,
ETloc (X)lo c2
, and relates to the partial data,
X[a1. . . an]
.
The ESP subtree of data
X
can be defined
EST(X,l,r)
as the sub-tree
ET(X)
that
comprises all
X[loc]
, such that
l≤loc ≤r
, plus all parent UAVs. Formally, we search and
discover UAVs of
ETloc (X)lo c2
, where
[l. . . r]∩range(ETloc (X)loc2)
6
=∅
. A name node is
derived from ETloc (X)loc2, which is loc,hXrange(ETloc(X)l oc2)∩[a. . . b)).
This results in an appropriate sub-tree of
ET(X)
, as a node is part of the sub-tree if
one of its children is counted in as a minimum. As stated earlier, we can define an array
that represents this ET.
Definition 3.
Define
AX(X,l,r)
as the characteristic array of
EST(X)
by similarity with
A(X)
; namely
AX(X,l,r)[x]
represents the the total times the partial data x are denoted as a
node in
EST(X,l,r)
. In this regard,
EST(X, 1, |X|)=ET(X)
; however, if not, generally
EST(X,l,r)=ET(X[l. . . r])
. Through
EST(X,l,r)
, it send the features of the edit-sensitive
parsing. Similar to Theorem 2, Theorem 4 is stated as follows.
Theorem 4.
Let
d
be
d(Y[lp. . . rp],X[lq. . . rq])
. Then,
d≤
2
||A.XY,lp,rp)−
A X(X,lq,rq])||1=O(logn log∗n)d.
Proof.
Definitely, as Lemma 9 does not assume anything regarding the tree structure,
the lower bound exists, meaning that the edit distance is simply double the length of the
difference amongst the ESP subtrees.
For the higher limit, assume implementing the required editing processes to the partial
data of
X
and
Y
. The impact on the ordinary ESP trees is observed,
ET(Y)
and
ET(X)
.
Theorem 2 verified that all editing processes could create a divergence of
O(lognlog∗n)
maximum among
A(X)
and
A(X0)
. Following this, the variance in
AS(X,l,r)
should be
limited as a result of similar volume: it seems impossible to remove additional UAVs, as the
UAVs of
EST(X,l,r)
is the subset of UAVs of
ET(X)
. Hence, as demonstrated in Theorem
2, the aggregate divergence 

A.XY,lp,rp−A.XX,lq,rq

1=d·O(lognlog∗n).
Lemma 10. A X(X,l+1, r+1)can be calculated from A X(X,l,r)in time O(log |X|).

Future Internet 2023,15, 279 15 of 24
Proof.
Remember that a UAV is contained within
EST(X,l,r)
once any dependent is
last-level analogous to
X[i]
contained when
i∈[l. . . r]
. It results in an easy method
for discovering
EST(X,l+1, r+1)
from
EST(X,l,r)
and
AX(X,l+1, r+1)
. We need
to eliminate
X
and some parents that do not cover
X[l]
from
EST(X,l,r)
to generate
AX(X,l+1, r+1).
Each parent
X
is adjusted to guarantee that its tag is accurate. The UAV located at
i(level) matching to the partial data
X[loc2. . . loc3]
, which is a parent of
X
, was earlier
denoted in the sub-tree via the
(loc,h(X[l. . . loc3]))
; it is required to be substituted with
(loc,h(X[l+1 . . . loc3])).
Suppose yis a UAV conforming to
X[r+1]
in
ET(X)
at the right. We add
y
to
EST(X,l+1, r)
to generate
EST(X,l+1, r+1)
, and we give the ancestor of
y
and desig-
nate her ancestor in
ET(X)
; give her the parent addition of your choice when it is absent.
Alter each parent of
y
to guarantee that their name is accurate: a parent of
y
corresponding
to the data
X[loc2. . . loc3]
will set
(loc,h(X[loc2. . . r+1]))
. As these circumstances, we
simply assume parents of a child UAV since the depth of tree is
O(log|X|)
, and this shows
that the process complexity with respect to time is O(log|X|).
4.4. Data Aggregation Level 2 Algorithm
Theorem 5.
Given a text,
t
, and string
s
, to resolve the data-matching issue with moves by calcu-
lating an
O(log n lo g∗n)
approximation to
D[loc]=min_loc ≤loc3≤n d(s,t[loc . . . loc3])
for
each loc in time O(n log n).
Proof. Our algorithm is as follows:
Given a dataset
X
of size m and dataset
Y
of size
n
, we calculate
ET(s)
and
ET(t)
in
time O(mlog∗n)as per Theorem 1.
Measure
EST(t, 1, m)
. This can be performed in the
O(n)
worst case, as a pre-order
traversal of
ET(t)
will be performed to determine which nodes are in
EST(t, 1, m)
. From
this, we can calculate
ˆ
D[1]||AX(t, 1, m)−AX(p, 1, m)||1
. We then recursively calculate
||AX(t,loc +1, loc +m)−AX(s, 1, m)||
1 from
||AX(t,loc,loc +m−1)−AX(s, 1, m)||
1 via
Lemma 7 to discover which nodes we need to add to or remove from
EST(t,loc,loc +m−1)
and regulate the total of the difference properly. 
This requires ncomparisons and will take
O(logn)
time for each. By Theorem 4 and
Lemma 9,
D[loc]≤ˆ
D[loc]≤O(lognlog∗n)D[loc]
. If
logn
is
O(logm)
, as one would expect
for some rational size string and text, then a tighter investigation demonstrates the running
time to be
O(nlogm)
. This is for the reason that we merely want to assume the lower
logm
levels of the parse trees; above, this
EST(t,loc,loc +m−1)
has only one node in each level.
Figure 5shows the flow of data aggregation Algorithm 2 to find the duplicated data in two
datasets, Xand Y.
Algorithm 2:
Data Aggregation Algorithm to Find the Duplicated Data in Two Datasets, Xand Y
Procedure Data_Match_with_Moves (DMM)
Input: Datasets, Xand Y
Output: True/False // Duplication Found or Not Found
1.
Initializations
i. Xlen←X.length()
ii. Ylen←Y.length ()
2. Allocate vector space V[0:m, 0:n].V[i,j] will contain the length of X[1:i] and Y[1:j].
3. V[0, j]←0 for all 0 ≤j≤nand V[i, 0] ←0 for all 0 ≤i≤m..Base Cases
4. for (i←1 to Xlen) then
5. for (j←0 to Ylen) then // matching the symbols from Xwith Ysymbols
6. if (j= 0) then // if Yis blank then eliminate all Xsymbols
// if symbol from both dataset is matching then no operation is required

Future Internet 2023,15, 279 16 of 24
Algorithm 2: Cont.
7. V[i% 2][j]←i;
8. else if (X[j−1] = Y[i−1]) then
9. V[i% 2][j]←V[(i−1) % 2][j−1];
10.
end else if
// if symbols from both datasets do not match, then we take the smallest from 3
operations.
// i.e., insert, delete and substitute
11. else then
12. V[i% 2][j]←1 + min(V[(i−1) % 2][j],
13. min(V[i% 2][j−1],
14. V[(i−1) % 2][j−1]));
15. end if
16. end for
17.
end for
// after filling the Vvector, if the size of Xlen is even, then
//we end up in the 0th row else
//we end up in the ith row, so we take Xlen % 2 to get row
18. P←V[Xlen % 2][Ylen] // the final value after matching two datasets
19. L←max (Xlen,Ylen )
20. if (P < L/2), then
21. return 1 // true value will return, i.e., duplication found
22. else then
23. return 0 // false value will return, i.e., duplication not found
24. end if
25. end procedure DMM
Future Internet 2023, 15, x FOR PEER REVIEW 17 of 25
15. end if
16. end for
17.
end for
// after filling the V vector, if the size of Xlen is even, then
//we end up in the 0th row else
//we end up in the ith row, so we take Xlen % 2 to get row
18. P←V[Xlen % 2][Ylen] // the final value after matching two datasets
19. L←max (Xlen, Ylen)
20. if (P<L/2), then
21. return 1 // true value will return, i.e., duplication found
22. else then
23. return 0 // false value will return
,
i.e.
,
duplication not found
24. end if
25. end procedure DMM
Figure 5. Data aggregation model.
5. Performance Evaluation and Simulation Study
The performance metrics for evaluating the proposed scheme were measured with
the mean packet delivery ratio (PDR), mean energy consumption, end-to-end delay, pack-
ets drop ratio, communication overhead, and bandwidth utilization [41–43]. The PDR is
the ratio of packets received by the receiver UAVs versus the packet sent by the sender
UAVs. The higher ratio means that the performance of the proposed scheme is beer. The
energy consumption shows the mean amount of energy consumed by the UAVs for data
transmission. The end-to-end delay means the time taken by the UAVs for packets’
Figure 5. Data aggregation model.

Future Internet 2023,15, 279 17 of 24
5. Performance Evaluation and Simulation Study
The performance metrics for evaluating the proposed scheme were measured with the
mean packet delivery ratio (PDR), mean energy consumption, end-to-end delay, packets
drop ratio, communication overhead, and bandwidth utilization [
41
–
43
]. The PDR is
the ratio of packets received by the receiver UAVs versus the packet sent by the sender
UAVs. The higher ratio means that the performance of the proposed scheme is better.
The energy consumption shows the mean amount of energy consumed by the UAVs for
data transmission. The end-to-end delay means the time taken by the UAVs for packets’
sending and receiving. It also measures the delay caused during route discovery and
waiting in a queue. The packet drop ratio means that the packets may be dropped during
the transmission, and it counts the ratio of the total number of packets received and
packets sent. Sometimes, the same packets or the additional information communicated
to the UAVs-CH reduces communication speed and consumes energy. The details of the
simulation parameters are given in Table 1.
Table 1. Simulation parameters.
Parameter Value
Network Simulator MATLAB
Covered Area 2 km ×2 km
MAC Protocol IEEE 802.11 and IEEE 802.16
Antenna Type Omni directional
Propagation Model Two-ray ground reflection model (intra-cluster)
Long-distance propagation loss model (inter-cluster)
Radio Frequency 2.4 GHz, 5 GHz
Number of UAVs 10 to 60
UAV Altitude 40–50 m
UAV Transmission Range 200 to 300 m
UAV Mobility Model Random waypoint model
Transport Protocol Stream control transmission protocol (SCTP)
Traffic Model Poisson traffic model
Application Packet Size 1000 Bytes
Initial Energy 2 to 5 J
Channel Model Multi-Propagation Channel (MPC) Model
The performance of the proposed redundant data elimination aggregation approach
was compared with non-redundant data elimination aggregation approaches, i.e., EE-UAV-
DA, OC-mUAV, and TA-UAV-DA. The data rate was fixed in the simulation, i.e., 250 Kbps,
and the number of UAVs varied from 10 to 60.
Figure 6shows the number of UAVs and the mean end-to-end delay. It is observed
that with the increase in UAVs, the proposed scheme has less of a mean delay as compared
to the EE-UAV-DA, OC-mUAV, and TA-UAV-DA. The FSNet-OC-DA uses HBA to form
clusters and data aggregation. Selecting optimized cluster heads has a strong impact on
end-to-end delay. The results show that our proposed scheme (FSNet-OC-DA) performs
better than other schemes under consideration.
Figure 7presents the number of UAVs vs. PDR. The simulation results show that,
initially, the PDR decreased with an increase in UAVs. The PDR of the proposed scheme
falls, while the EE-UAV-DA, OC-mUAV, and TA-UAV-DA have more decreases than our
proposed algorithm. The impact of optimum cluster formation using HBA reflects that
once optimized cluster heads are selected, this will increase the PDR. This is because the
cluster heads belong to optimal zones with high energy, relative mobility, and high density.

Future Internet 2023,15, 279 18 of 24
As the packets are routed via cluster heads, the proposed scheme with optimal cluster
heads performs better than others.
Future Internet 2023, 15, x FOR PEER REVIEW 18 of 25
sending and receiving. It also measures the delay caused during route discovery and wait-
ing in a queue. The packet drop ratio means that the packets may be dropped during the
transmission, and it counts the ratio of the total number of packets received and packets
sent. Sometimes, the same packets or the additional information communicated to the
UAVs-CH reduces communication speed and consumes energy. The details of the simu-
lation parameters are given in Table 1.
Table 1. Simulation parameters.
Parameter Value
Network Simulator MATLAB
Covered Area 2 Km × 2 Km
MAC Protocol IEEE 802.11 and IEEE 802.16
Antenna Type Omni directional
Propagation Model Two-ray ground reflection model (intra-cluster)
Long-distance propagation loss model (inter-cluster)
Radio Frequency 2.4 GHz, 5 GHz
Number of UAVs 10 to 60
UAV Altitude 40–50 m
UAV Transmission Range 200 to 300 m
UAV Mobility Model Random waypoint model
Transport Protocol Stream control transmission protocol (SCTP)
Traffic Model Poisson traffic model
Application Packet Size 1000 Bytes
Initial Energy 2 to 5 j
Channel Model Multi-Propagation Channel (MPC) Model
The performance of the proposed redundant data elimination aggregation approach
was compared with non-redundant data elimination aggregation approaches, i.e., EE-
UAV-DA, OC-mUAV, and TA-UAV-DA. The data rate was fixed in the simulation, i.e., 250
kbps, and the number of UAVs varied from 10 to 60.
Figure 6 shows the number of UAVs and the mean end-to-end delay. It is observed
that with the increase in UAVs, the proposed scheme has less of a mean delay as compared
to the EE-UAV-DA, OC-mUAV, and TA-UAV-DA. The FSNet-OC-DA uses HBA to form
clusters and data aggregation. Selecting optimized cluster heads has a strong impact on
end-to-end delay. The results show that our proposed scheme (FSNet-OC-DA) performs
beer than other schemes under consideration.
Figure 6. Number of UAVs vs. end-to-end delay.
Figure 6. Number of UAVs vs. end-to-end delay.
Future Internet 2023, 15, x FOR PEER REVIEW 19 of 25
Figure 7 presents the number of UAVs vs. PDR. The simulation results show that,
initially, the PDR decreased with an increase in UAVs. The PDR of the proposed scheme
falls, while the EE-UAV-DA, OC-mUAV, and TA-UAV-DA have more decreases than our
proposed algorithm. The impact of optimum cluster formation using HBA reflects that
once optimized cluster heads are selected, this will increase the PDR. This is because the
cluster heads belong to optimal zones with high energy, relative mobility, and high den-
sity. As the packets are routed via cluster heads, the proposed scheme with optimal cluster
heads performs beer than others.
Figure 7. Number of UAVs vs. PDR.
Figure 8 illustrates the number of UAVs and packet drop ratio of the proposed
scheme and other existing approaches. The simulation result shows that the drop ratio
increased in the existing methods and our proposed scheme with the increase in UAVs.
The packet drop ratio increased in all schemes because, in dense networks, the number of
packets increases, and the load on other nodes also increases. This results in packet drops
because the nodes are overloaded. The packet drop in our proposed scheme is less than
others because we optimized cluster formation using HBA.
Figure 8. Number of UAVs vs. packet drop ratio.
The increase in the number of UAVs has a direct impact on residual energy. Figure 9
shows that the proposed FSNet-OC-DA residual energy (recorded in round 10) is beer
than all existing approaches. The proposed scheme eliminates duplicate data transmission
to the UAVS-CH by using a near-linear time algorithm. Eliminating data reduces long-
distance communication. As we already know, communication consumes more energy
than computation. Our model focuses on optimization and reduces communication costs.
Figure 7. Number of UAVs vs. PDR.
Figure 8illustrates the number of UAVs and packet drop ratio of the proposed scheme
and other existing approaches. The simulation result shows that the drop ratio increased in
the existing methods and our proposed scheme with the increase in UAVs. The packet drop
ratio increased in all schemes because, in dense networks, the number of packets increases,
and the load on other nodes also increases. This results in packet drops because the nodes
are overloaded. The packet drop in our proposed scheme is less than others because we
optimized cluster formation using HBA.
Future Internet 2023, 15, x FOR PEER REVIEW 19 of 25
Figure 7 presents the number of UAVs vs. PDR. The simulation results show that,
initially, the PDR decreased with an increase in UAVs. The PDR of the proposed scheme
falls, while the EE-UAV-DA, OC-mUAV, and TA-UAV-DA have more decreases than our
proposed algorithm. The impact of optimum cluster formation using HBA reflects that
once optimized cluster heads are selected, this will increase the PDR. This is because the
cluster heads belong to optimal zones with high energy, relative mobility, and high den-
sity. As the packets are routed via cluster heads, the proposed scheme with optimal cluster
heads performs beer than others.
Figure 7. Number of UAVs vs. PDR.
Figure 8 illustrates the number of UAVs and packet drop ratio of the proposed
scheme and other existing approaches. The simulation result shows that the drop ratio
increased in the existing methods and our proposed scheme with the increase in UAVs.
The packet drop ratio increased in all schemes because, in dense networks, the number of
packets increases, and the load on other nodes also increases. This results in packet drops
because the nodes are overloaded. The packet drop in our proposed scheme is less than
others because we optimized cluster formation using HBA.
Figure 8. Number of UAVs vs. packet drop ratio.
The increase in the number of UAVs has a direct impact on residual energy. Figure 9
shows that the proposed FSNet-OC-DA residual energy (recorded in round 10) is beer
than all existing approaches. The proposed scheme eliminates duplicate data transmission
to the UAVS-CH by using a near-linear time algorithm. Eliminating data reduces long-
distance communication. As we already know, communication consumes more energy
than computation. Our model focuses on optimization and reduces communication costs.
Figure 8. Number of UAVs vs. packet drop ratio.

Future Internet 2023,15, 279 19 of 24
The increase in the number of UAVs has a direct impact on residual energy. Figure 9
shows that the proposed FSNet-OC-DA residual energy (recorded in round 10) is better
than all existing approaches. The proposed scheme eliminates duplicate data transmission
to the UAVS-CH by using a near-linear time algorithm. Eliminating data reduces long-
distance communication. As we already know, communication consumes more energy than
computation. Our model focuses on optimization and reduces communication costs. The
efficient optimization and data aggregation enable nodes to consume less energy. Hence,
FSNet-OC-DA energy consumption is better than the other schemes.
Future Internet 2023, 15, x FOR PEER REVIEW 20 of 25
The efficient optimization and data aggregation enable nodes to consume less energy.
Hence, FSNet-OC-DA energy consumption is beer than the other schemes.
Figure 9. Number of UAVs vs. residual energy.
Figure 10 shows that the communication overhead increases with the increase in
UAVs, but the FSNet-OC-DA has significantly less communication overhead. The number
of UAVs in each cluster is fixed in the simulation, i.e., 40, and the data rate varies from 50
to 250 Kbps. Figure 11 represents the UAVs’ data rate and end-to-end delay of the FSNet-
OC-DA, EE-UAV-DA, OC-mUAV, and TA-UAV-DA. The simulation result in Figure 10
shows that the end-to-end delay increases with the increase in data rates from 50 to 250
Kbps. It is observed that the FSNet-OC-DA has less end-to-end delay than the existing
approaches. The PDR for different data rates (50 to 250 Kbps) is represented in Figure 12.
Initially, when the data rate is 50 Kbps, the PDR is very high, but the delivery ratio de-
creases gradually with the increase in the data rate.
Figure 10. Number of UAVs vs. message overhead.
Figure 9. Number of UAVs vs. residual energy.
Figure 10 shows that the communication overhead increases with the increase in
UAVs, but the FSNet-OC-DA has significantly less communication overhead. The number
of UAVs in each cluster is fixed in the simulation, i.e., 40, and the data rate varies from 50 to
250 Kbps. Figure 11 represents the UAVs’ data rate and end-to-end delay of the FSNet-OC-
DA, EE-UAV-DA, OC-mUAV, and TA-UAV-DA. The simulation result in Figure 10 shows
that the end-to-end delay increases with the increase in data rates from 50 to 250 Kbps. It is
observed that the FSNet-OC-DA has less end-to-end delay than the existing approaches.
The PDR for different data rates (50 to 250 Kbps) is represented in Figure 12. Initially, when
the data rate is 50 Kbps, the PDR is very high, but the delivery ratio decreases gradually
with the increase in the data rate.
Future Internet 2023, 15, x FOR PEER REVIEW 20 of 25
The efficient optimization and data aggregation enable nodes to consume less energy.
Hence, FSNet-OC-DA energy consumption is beer than the other schemes.
Figure 9. Number of UAVs vs. residual energy.
Figure 10 shows that the communication overhead increases with the increase in
UAVs, but the FSNet-OC-DA has significantly less communication overhead. The number
of UAVs in each cluster is fixed in the simulation, i.e., 40, and the data rate varies from 50
to 250 Kbps. Figure 11 represents the UAVs’ data rate and end-to-end delay of the FSNet-
OC-DA, EE-UAV-DA, OC-mUAV, and TA-UAV-DA. The simulation result in Figure 10
shows that the end-to-end delay increases with the increase in data rates from 50 to 250
Kbps. It is observed that the FSNet-OC-DA has less end-to-end delay than the existing
approaches. The PDR for different data rates (50 to 250 Kbps) is represented in Figure 12.
Initially, when the data rate is 50 Kbps, the PDR is very high, but the delivery ratio de-
creases gradually with the increase in the data rate.
Figure 10. Number of UAVs vs. message overhead.
Figure 10. Number of UAVs vs. message overhead.

Future Internet 2023,15, 279 20 of 24
Future Internet 2023, 15, x FOR PEER REVIEW 21 of 25
Figure 11. UAVs’ data rate vs. end-to-end delay.
Figure 12. UAVs’ data rate vs. PDR.
Figure 13 shows that, initially, the UAVs’ data rate is 50 Kbps, and the packet drop
ratio is very minimal. Still, with the increase in the UAVs’ data rate, the packet drop ratio
increases up to the highest level. The FSNet-OC-DA packet drop ratio is always lower
when the data rate varies from 50 to 250 Kbps.
Figure 13. UAVs’ data rate vs. packet drop ratio.
Figure 14 represents the data rate and residual energy of UAVs. The residual energy
decreases with the increase in the data rate of UAVs. The remaining residual energy of the
FSNet-OC-DA is still beer among other existing approaches.
Figure 11. UAVs’ data rate vs. end-to-end delay.
Future Internet 2023, 15, x FOR PEER REVIEW 21 of 25
Figure 11. UAVs’ data rate vs. end-to-end delay.
Figure 12. UAVs’ data rate vs. PDR.
Figure 13 shows that, initially, the UAVs’ data rate is 50 Kbps, and the packet drop
ratio is very minimal. Still, with the increase in the UAVs’ data rate, the packet drop ratio
increases up to the highest level. The FSNet-OC-DA packet drop ratio is always lower
when the data rate varies from 50 to 250 Kbps.
Figure 13. UAVs’ data rate vs. packet drop ratio.
Figure 14 represents the data rate and residual energy of UAVs. The residual energy
decreases with the increase in the data rate of UAVs. The remaining residual energy of the
FSNet-OC-DA is still beer among other existing approaches.
Figure 12. UAVs’ data rate vs. PDR.
Figure 13 shows that, initially, the UAVs’ data rate is 50 Kbps, and the packet drop
ratio is very minimal. Still, with the increase in the UAVs’ data rate, the packet drop ratio
increases up to the highest level. The FSNet-OC-DA packet drop ratio is always lower
when the data rate varies from 50 to 250 Kbps.
Future Internet 2023, 15, x FOR PEER REVIEW 21 of 25
Figure 11. UAVs’ data rate vs. end-to-end delay.
Figure 12. UAVs’ data rate vs. PDR.
Figure 13 shows that, initially, the UAVs’ data rate is 50 Kbps, and the packet drop
ratio is very minimal. Still, with the increase in the UAVs’ data rate, the packet drop ratio
increases up to the highest level. The FSNet-OC-DA packet drop ratio is always lower
when the data rate varies from 50 to 250 Kbps.
Figure 13. UAVs’ data rate vs. packet drop ratio.
Figure 14 represents the data rate and residual energy of UAVs. The residual energy
decreases with the increase in the data rate of UAVs. The remaining residual energy of the
FSNet-OC-DA is still beer among other existing approaches.
Figure 13. UAVs’ data rate vs. packet drop ratio.
Figure 14 represents the data rate and residual energy of UAVs. The residual energy
decreases with the increase in the data rate of UAVs. The remaining residual energy of the
FSNet-OC-DA is still better among other existing approaches.
Figure 15 represents the UAVs’ data rate and the ratio of the message overhead. The
non-redundant data elimination approaches’ communication overhead is higher than the
proposed redundant data elimination schemes. Bandwidth is the capacity of commu-
nication channels among the UAVs. The bandwidth occupancy rate is the ratio of the

Future Internet 2023,15, 279 21 of 24
bandwidth used by the redundant data elimination aggregation approach and without
redundant aggregation approaches.
Future Internet 2023, 15, x FOR PEER REVIEW 22 of 25
Figure 14. UAVs’ data rate vs. residual energy.
Figure 15 represents the UAVs’ data rate and the ratio of the message overhead. The
non-redundant data elimination approaches’ communication overhead is higher than the
proposed redundant data elimination schemes. Bandwidth is the capacity of communica-
tion channels among the UAVs. The bandwidth occupancy rate is the ratio of the band-
width used by the redundant data elimination aggregation approach and without redun-
dant aggregation approaches.
Figure 15. UAVs’ data rate vs. message overhead.
Figure 16 represents the bandwidth occupancy and redundancy rate of each UAV.
The bandwidth occupancy of the FSNet-OC-DA is moving towards close to zero com-
pared to the existing approaches. In FSNet-OC-DA, the UAVs avoid redundant data and
transmit only actual data to a UAVS-CH. At the same time, the conventional data aggre-
gation approaches utilize (50) percent bandwidth of the total available bandwidth.
Figure 14. UAVs’ data rate vs. residual energy.
Future Internet 2023, 15, x FOR PEER REVIEW 22 of 25
Figure 14. UAVs’ data rate vs. residual energy.
Figure 15 represents the UAVs’ data rate and the ratio of the message overhead. The
non-redundant data elimination approaches’ communication overhead is higher than the
proposed redundant data elimination schemes. Bandwidth is the capacity of communica-
tion channels among the UAVs. The bandwidth occupancy rate is the ratio of the band-
width used by the redundant data elimination aggregation approach and without redun-
dant aggregation approaches.
Figure 15. UAVs’ data rate vs. message overhead.
Figure 16 represents the bandwidth occupancy and redundancy rate of each UAV.
The bandwidth occupancy of the FSNet-OC-DA is moving towards close to zero com-
pared to the existing approaches. In FSNet-OC-DA, the UAVs avoid redundant data and
transmit only actual data to a UAVS-CH. At the same time, the conventional data aggre-
gation approaches utilize (50) percent bandwidth of the total available bandwidth.
Figure 15. UAVs’ data rate vs. message overhead.
Figure 16 represents the bandwidth occupancy and redundancy rate of each UAV. The
bandwidth occupancy of the FSNet-OC-DA is moving towards close to zero compared to
the existing approaches. In FSNet-OC-DA, the UAVs avoid redundant data and transmit
only actual data to a UAVS-CH. At the same time, the conventional data aggregation
approaches utilize (50) percent bandwidth of the total available bandwidth.
Future Internet 2023, 15, x FOR PEER REVIEW 23 of 25
Figure 16. Redundancy rate vs. bandwidth occupancy.
6. Conclusions and Future Work
Sensors and UAVs have made it easier to monitor, observe, and share information
about an area of interest remotely. The researchers proposed energy-efficient schemes by
considering different parameters, such as reducing communication distance, computation
cost, mobility, and degree. However, data collection minimizes the communication load
to save bandwidth and energy.
In this study, the honeybee foraging property was first used to select the optimal CH
set and form stable and balanced clusters. The modified HBA selects UAVs-CH based on
residual energy, UAV degree, and relative mobility. To transmit data, the UAV connects
to the nearest CH. Ordinary UAVs choose CH randomly if they have the same distance
with more than one CH. The reaffiliation rate will decrease with the proposed stable clus-
tering procedure. Secondly, ordinary UAVs transmit data to their CH once clusters are
formed. An aggregation method based on dynamic programming is proposed to save en-
ergy consumption and bandwidth. The data aggregation procedure is applied at the clus-
ter level to minimize communication and save bandwidth and energy. Simulation exper-
iments validate the proposed FSNet-OC-DA. FSNet-OC-DA is compared with non-redun-
dant data elimination and aggregation approaches, such as EE-UAV-DA, OC-mUAV, and
TA-UAV-DA, in terms of the end-to-end delay, PDR, packet drop ratio, residual energy,
communication overhead, bandwidth occupancy with varying numbers of UAVs, data
rate, and redundancy rate. The simulation results show that our proposed FSNet-OC-DA
outperforms state-of-the-art cluster-based data aggregation schemes.
Author Contributions: Conceptualization, M.A.; methodology A.S. and Q.J.; software, A.S. and I.W.;
validation, A.S. and M.Y.A.; draft preparation, A.S., M.Y.A., and I.W.; review and editing, M.A. and
I.W.; visualization, A.S.; supervision, Q.J.; funding acquisition, M.Y.A. All authors have read and
agreed to the published version of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: Data will be made available on request.
Acknowledgments: The authors wish to thank the editor and anonymous referees for their helpful
comments on improving the quality of this paper.
Conflicts of Interest: The authors declare that we have no conflicts of interest regarding the publi-
cation of this article.
References
1. Alam, M.M.; Arafat, M.Y.; Moh, S.; Shen, J. Topology control algorithms in multi-unmanned aerial vehicle networks: An exten-
sive survey. J. Netw. Comput. Appl. 2022, 207, 103495. hps://doi.org/10.1016/j.jnca.2022.103495.
Figure 16. Redundancy rate vs. bandwidth occupancy.

Future Internet 2023,15, 279 22 of 24
6. Conclusions and Future Work
Sensors and UAVs have made it easier to monitor, observe, and share information
about an area of interest remotely. The researchers proposed energy-efficient schemes by
considering different parameters, such as reducing communication distance, computation
cost, mobility, and degree. However, data collection minimizes the communication load to
save bandwidth and energy.
In this study, the honeybee foraging property was first used to select the optimal CH
set and form stable and balanced clusters. The modified HBA selects UAVs-CH based on
residual energy, UAV degree, and relative mobility. To transmit data, the UAV connects
to the nearest CH. Ordinary UAVs choose CH randomly if they have the same distance
with more than one CH. The reaffiliation rate will decrease with the proposed stable
clustering procedure. Secondly, ordinary UAVs transmit data to their CH once clusters
are formed. An aggregation method based on dynamic programming is proposed to save
energy consumption and bandwidth. The data aggregation procedure is applied at the
cluster level to minimize communication and save bandwidth and energy. Simulation
experiments validate the proposed FSNet-OC-DA. FSNet-OC-DA is compared with non-
redundant data elimination and aggregation approaches, such as EE-UAV-DA, OC-mUAV,
and TA-UAV-DA, in terms of the end-to-end delay, PDR, packet drop ratio, residual energy,
communication overhead, bandwidth occupancy with varying numbers of UAVs, data
rate, and redundancy rate. The simulation results show that our proposed FSNet-OC-DA
outperforms state-of-the-art cluster-based data aggregation schemes.
Author Contributions:
Conceptualization, M.A.; methodology A.S. and Q.J.; software, A.S. and I.W.;
validation, A.S. and M.Y.A.; draft preparation, A.S., M.Y.A. and I.W.; review and editing, M.A. and
I.W.; visualization, A.S.; supervision, Q.J.; funding acquisition, M.Y.A. All authors have read and
agreed to the published version of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: Data will be made available on request.
Acknowledgments:
The authors wish to thank the editor and anonymous referees for their helpful
comments on improving the quality of this paper.
Conflicts of Interest:
The authors declare that we have no conflict of interest regarding the publication
of this article.
References
1.
Alam, M.M.; Arafat, M.Y.; Moh, S.; Shen, J. Topology control algorithms in multi-unmanned aerial vehicle networks: An extensive
survey. J. Netw. Comput. Appl. 2022,207, 103495. [CrossRef]
2. Sarkar, N.I.; Gul, S. Artificial Intelligence-Based Autonomous UAV Networks: A Survey. Drones 2023,7, 322. [CrossRef]
3.
Abu-Baker, A.; Shakhatreh, H.; Sawalmeh, A.; Alenezi, A.H. Efficient data collection in UAV-assisted cluster-based wireless
sensor networks for 3D Environment: Optimization Study. J. Sens. 2023,2023, 9513868. [CrossRef]
4.
Luo, X.; Chen, C.; Zeng, C.; Li, C.; Xu, J.; Gong, S. Deep Reinforcement Learning for Joint Trajectory Planning, Transmission
Scheduling, and Access Control in UAV-Assisted Wireless Sensor Networks. Sensors 2023,23, 4691. [CrossRef] [PubMed]
5. Ahmad, S.; Zhang, J.; Khan, A.; Khan, U.A.; Hayat, B. JO-TADP: Learning-Based Cooperative Dynamic Resource Allocation for
MEC–UAV-Enabled Wireless Network. Drones 2023,7, 303. [CrossRef]
6.
Zhou, R.; Zhang, X.; Song, D.; Qin, K.; Xu, L. Topology Duration Optimization for UAV Swarm Network under the System
Performance Constraint. Appl. Sci. 2023,13, 5602. [CrossRef]
7.
Salam, A.; Javaid, Q.; Ali, G.; Ahmad, F.; Ahmad, M.; Wahid, I. Flying Sensor Network optimization using Bee Intelligence for
internet of things. In Advances in Intelligent Systems and Computing, Proceedings of the International Conference on Computer Science
and Information Technologies, Zbarazh, Ukraine, 23–26 September 2020; Springer: Cham, Switzerland, 2020; Volume 1252, pp. 331–339.
8.
Chen, T.; Dong, F.; Ye, H.; Wang, Y.; Wu, B. Data Collection Mechanism for UAV-Assisted Cellular Network Based on PPO.
Electronics 2023,12, 1376. [CrossRef]
9.
Amodu, O.A.; Nordin, R.; Jarray, C.; Bukar, U.A.; Raja Mahmood, R.A.; Othman, M. A Survey on the Design Aspects and
Opportunities in Age-Aware UAV-Aided Data Collection for Sensor Networks and Internet of Things Applications. Drones
2023
,
7, 260. [CrossRef]
10.
Xiong, J.; Li, Z.; Li, H.; Tang, L.; Zhong, S. Energy-Constrained UAV Data Acquisition in Wireless Sensor Networks with the Age
of Information. Electronics 2023,12, 1739. [CrossRef]

Future Internet 2023,15, 279 23 of 24
11.
Kim, T.; Lee, S.; Kim, K.H.; Jo, Y.-I. FANET Routing Protocol Analysis for Multi-UAV-Based Reconnaissance Mobility Models.
Drones 2023,7, 161. [CrossRef]
12.
Arafat, M.Y.; Moh, S. JRCS: Joint Routing and charging strategy for logistics drones. IEEE Int. Things J.
2022
,9, 21751–21764.
[CrossRef]
13.
Arafat, M.Y.; Habib, M.A.; Moh, S. Routing Protocols for UAV-Aided Wireless Sensor Networks. Appl. Sci.
2020
,10, 4077.
[CrossRef]
14.
Noh, K.-L.; Wu, Y.-C.; Qaraqe, K.; Suter, B.W. Extension of pairwise broadcast clock synchronization for Multicluster sensor
networks. EURASIP J. Adv. Signal Process. 2008,2007, 286168. [CrossRef]
15.
Cheng, K.-Y.; Lui, K.-S.; Wu, Y.-C.; Tam, V. A distributed Multihop Time Synchronization Protocol for wireless sensor networks
using pairwise broadcast synchronization. IEEE Trans. Wirel. Commun. 2009,8, 1764–1772. [CrossRef]
16.
Alam, M.M.; Moh, S. Survey on Q-Learning-Based Position-Aware Routing Protocols in Flying Ad Hoc Networks. Electronics
2022,11, 1099. [CrossRef]
17.
Xiong, F.; Zheng, H.; Ruan, L.; Wang, H.; Tang, L.; Dong, X.; Li, A. Energy-saving data aggregation for Multi-UAV system. IEEE
Trans. Veh. Technol. 2020,69, 9002–9016. [CrossRef]
18.
Aadil, F.; Raza, A.; Khan, M.F.; Maqsood, M.; Mehmood, I.; Rho, S. Energy Aware Cluster-Based Routing in Flying Ad-Hoc
Networks. Sensors 2018,18, 1413. [CrossRef]
19.
Arafat, M.Y.; Moh, S. Localization and clustering based on swarm intelligence in UAV Networks for Emergency Communications.
IEEE Internet Things J. 2019,6, 8958–8976. [CrossRef]
20.
Yang, J.; Wang, X.; Li, Z.; Yang, P.; Luo, X.; Zhang, K.; Zhang, S.; Chen, L. Path planning of unmanned aerial vehicles for farmland
information monitoring based on WSN. In Proceedings of the 2016 12th World Congress on Intelligent Control and Automation
(WCICA) 2016, Guilin, China, 12–15 June 2016.
21.
Yu, Y.; Ru, L.; Chi, W.; Liu, Y.; Yu, Q.; Fang, K. Ant colony optimization based polymorphism-aware routing algorithm for ad hoc
UAV network. Multimed. Tools Appl. 2016,75, 14451–14476. [CrossRef]
22.
Holtorf, L.; Titov, I.; Daschner, F.; Gerken, M. UAV-Based Wireless Data Collection from Underground Sensor Nodes for Precision
Agriculture. AgriEngineering 2023,5, 338–354. [CrossRef]
23.
Zhang, X.; Cao, Y. Memetic Algorithm with Isomorphic Transcoding for UAV Deployment Optimization in Energy-Efficient AIoT
Data Collection. Mathematics 2022,10, 4668. [CrossRef]
24.
Bharany, S.; Sharma, S.; Frnda, J.; Shuaib, M.; Khalid, M.I.; Hussain, S.; Iqbal, J.; Ullah, S.S. Wildfire Monitoring Based on Energy
Efficient Clustering Approach for FANETS. Drones 2022,6, 193. [CrossRef]
25.
Wang, X.; Zhou, Q.; Cheng, C.-T. A UAV-assisted topology-aware data aggregation protocol in WSN. Phys. Commun.
2019
,34,
48–57. [CrossRef]
26.
Wu, Q.; Sun, P.; Boukerche, A. An energy-efficient UAV-based data aggregation protocol in Wireless Sensor Networks. In
Proceedings of the 8th ACM Symposium on Design and Analysis of Intelligent Vehicular Networks and Applications 2018,
Montreal, QC, Canada, 28 October—2 November 2018; pp. 34–40.
27.
Thammawichai, M.; Baliyarasimhuni, S.P.; Kerrigan, E.C.; Sousa, J.B. Optimizing Communication and computation for Multi-UAV
information gathering applications. IEEE Trans. Aerosp. Electron. Syst. 2018,54, 601–615. [CrossRef]
28.
Dong, M.; Ota, K.; Lin, M.; Tang, Z.; Du, S.; Zhu, H. UAV-Assisted Data Gathering in wireless sensor networks. J. Supercomput.
2014,70, 1142–1155. [CrossRef]
29.
Liu, B.; Zhu, H. Energy-Effective Data Gathering for UAV-Aided Wireless Sensor Networks. Sensors
2019
,19, 2506. [CrossRef]
[PubMed]
30.
Cvetkovi´c, A.; Blagojevi ´c, V.; Manojlovi ´c, J. Capacity Analysis of Power Beacon-Assisted Industrial IoT System with UAV Data
Collector. Drones 2023,7, 146. [CrossRef]
31.
Cao, J.; Zhu, X.; Sun, S.; Wei, Z.; Jiang, Y.; Wang, J.; Lau, V.K.N. Toward industrial metaverse: Age of information, latency and
reliability of short-packet transmission in 6G. IEEE Wirel. Commun. 2023,30, 40–47. [CrossRef]
32.
Li, Z.; Zhao, W.; Liu, C. Completion Time Minimization for UAV-UGV-Enabled Data Collection. Sensors
2022
,22, 5839. [CrossRef]
33.
Nie, M.; Huang, P.; Zeng, J.; Lu, Y.; Zhang, T.; Lv, T. A Novel Dynamic Transmission Power of Cluster Heads Based Clustering
Scheme. Electronics 2023,12, 619. [CrossRef]
34.
Zhang, M.; Li, J.; Wu, X.; Wang, X. Coalition Game Based Distributed Clustering Approach for Group Oriented Unmanned Aerial
Vehicle Networks. Drones 2023,7, 91. [CrossRef]
35.
Mehmood, A.; Iqbal, Z.; Shah, A.A.; Maple, C.; Lloret, J. An Intelligent Cluster-Based Communication System for Multi-Unmanned
Aerial Vehicles for Searching and Rescuing. Electronics 2023,12, 607. [CrossRef]
36.
Chen, G.; Chen, G. A Method of Relay Node Selection for UAV Cluster Networks Based on Distance and Energy Constraints.
Sustainability 2022,14, 16089. [CrossRef]
37.
Salam, A.; Javaid, Q.; Ahmad, M. Bioinspired mobility-aware clustering optimization in flying ad hoc sensor network for internet
of things: Bimac-FASNET. Complexity 2020,2020, 9797650. [CrossRef]
38.
Cormode, G.; Muthukrishnan, S. The string edit distance matching problem with moves. ACM Trans. Algorithms
2007
,3, 1–19.
[CrossRef]

Future Internet 2023,15, 279 24 of 24
39.
Shapira, D.; Storer, J.A. Edit Distance with Move Operations. In Combinatorial Pattern Matching, Proceedings of the CPM 2002,
Fukuoka, Japan, 3–5 July 2002; Lecture Notes in Computer Science; Apostolico, A., Takeda, M., Eds.; Springer: Berlin/Heidelberg,
Germany, 2002; Volume 2373, p. 2373. [CrossRef]
40.
Maruyama, S.; Nakahara, M.; Kishiue, N.; Sakamoto, H. ESP-index: A compressed index based on edit-sensitive parsing. J.
Discrete Algorithms 2013,18, 100–112. [CrossRef]
41.
Wheeb, A.H.; Nordin, R.; Samah, A.A.; Kanellopoulos, D. Performance Evaluation of Standard and Modified OLSR Protocols for
Uncoordinated UAV Ad-Hoc Networks in Search and Rescue Environments. Electronics 2023,12, 1334. [CrossRef]
42.
Liu, P.; Wang, X.; Hawbani, A.; Busaileh, O.; Zhao, L.; Al-Dubai, A. FRCA: A novel flexible routing computing approach for
wireless sensor networks. IEEE Trans. Mob. Comput. 2020,19, 2623–2639. [CrossRef]
43.
Hu, Y.; Liu, Y.; Kaushik, A.; Masouros, C.; Thompson, J. Timely data collection for UAV-based IOT Networks: A deep reinforcement
learning approach. IEEE Sens. J. 2023,23, 12295–12308. [CrossRef]
Disclaimer/Publisher’s Note:
The statements, opinions and data contained in all publications are solely those of the individual
author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to
people or property resulting from any ideas, methods, instructions or products referred to in the content.