A Novelty of Hypergraph Clustering Model (HGCM) for Urban Scenario in VANET

Abstract

A vehicular ad hoc network is a dynamic and constantly changing topology that requires reliable clustering to prevent connection failure. A stable cluster head (CH) prevents packet delay (PD) and maintains high throughput in the network. This article presents a twofold novel scheme for stable CH selection. In the first part of the proposed scheme, the vehicle network is considered a one-to-many connection network, which is near to a practical scenario. The cluster generation is handled using a newly proposed vehicular-hypergraph-based spectral clustering model. In the second part, the CH is selected considering the criteria for maintaining a stable connection with the maximum number of neighbours. The new rewarding/penalising relative speed and neighbourhood degree fulfil the condition. Eccentricity assesses that the vehicle should be at the centre of the cluster. Another metric with deep learning spectrum sensing is introduced for CH selection. Trust calculation is performed using deep learning-trained spectrum sensing as a model. The primary vehicle in noisy and noiseless environments is recognised using layers of long short-term memory. A high trust score is awarded to the vehicle which vacates the spectrum in the sensing of the primary vehicle. The stable CH selected by these metrics reduces the overhead that occurs due to the frequent shifting of the CH from one vehicle to another. This has been validated by the improved CH stability; increased cluster member (CM) lifetime and reduced rate of change of CH. The proposed scheme also demonstrates a considerable improvement in PD and throughput. INDEX TERMS Cluster head stability, eccentricity, hypergraph, trust, VANET.

Full text

Received 21 May 2022, accepted 16 June 2022, date of publication 21 June 2022, date of current version 27 June 2022.
Digital Object Identifier 10.1109/ACCESS.2022.3185075
A Novelty of Hypergraph Clustering
Model (HGCM) for Urban Scenario in VANET
MAYS KAREEM JABBAR 1,2 AND HAFEDH TRABELSI1
1CES Laboratory, École Nationale d’Ingénieurs de Sfax (ENIS), University of Sfax, Sfax 3029, Tunisia
2Faculty of Engineering, University of Misan, Amarah, Misan 62001, Iraq
Corresponding author: Mays Kareem Jabbar (m_mays85@uomisan.edu.iq)
ABSTRACT A vehicular ad hoc network is a dynamic and constantly changing topology that requires reliable
clustering to prevent connection failure. A stable cluster head (CH) prevents packet delay (PD) and maintains
high throughput in the network. This article presents a two-fold novel scheme for stable CH selection. In the
first part of the proposed scheme, the vehicle network is considered a one-to-many connection network,
which is near to a practical scenario. The cluster generation is handled using a newly proposed vehicular-
hypergraph-based spectral clustering model. In the second part, the CH is selected considering the criteria for
maintaining a stable connection with the maximum number of neighbours. The new rewarding/penalising
relative speed and neighbourhood degree fulfil the condition. Eccentricity assesses that the vehicle should
be at the centre of the cluster. Another metric with deep learning spectrum sensing is introduced for CH
selection. Trust calculation is performed using deep learning-trained spectrum sensing as a model. The
primary vehicle in noisy and noiseless environments is recognised using layers of long short-term memory.
A high trust score is awarded to the vehicle which vacates the spectrum in the sensing of the primary vehicle.
The stable CH selected by these metrics reduces the overhead that occurs due to the frequent shifting
of the CH from one vehicle to another. This has been validated by the improved CH stability; increased
cluster member (CM) lifetime and reduced rate of change of CH. The proposed scheme also demonstrates a
considerable improvement in PD and throughput.
INDEX TERMS Cluster head stability, eccentricity, hypergraph, trust, VANET.
I. INTRODUCTION
A. BACKGROUND
A vehicular ad hoc network (VANET) is an amalgama-
tion of existing ad hoc networks, wireless LAN and cellu-
lar technology to achieve road traffic safety and efficiency.
VANETs stand out due to their hybrid network architecture,
node movement and various application scenarios. There-
fore, these networks pose several unique networking research
challenges [1]. VANETs are amongst the significant appli-
cations of intelligent transportation systems. They include
various applications, such as cooperative traffic monitoring,
control of traffic flows, blind crossing, prevention of colli-
sions, nearby information services and real-time detour route
computation[2].
VANETs have a highly dynamic topology, with a high
relative speed of vehicles and frequent discontinuity in the
networks. The topology management in VANETs can be
The associate editor coordinating the review of this manuscript and
approving it for publication was Mauro Tucci .
achieved through clustering. To manage the topology, similar
moving speed vehicles are grouped. The more effective is the
clustering, the better is the topology control [3]. Each cluster
has a CH that communicates with the external controlling
stations such as the road side unit (RSU) [4]. The vehicles are
grouped based on either their location or user information,
such as direction and speed. Both approaches are based on
mathematical formulation, leaving behind the sociological
aspects of how the driver will change the lane and his desti-
nations. Cluster generation and maintenance are a distributed
approach. However, cluster generation is considered cen-
tralised by many researchers [5]. Likewise, many challenges
are faced in an urban scenario as the heavy intersection of
roads, concrete infrastructure and heavy density of vehicles
lead to variable topology and mobility with time dependency.
The weak communication link is another major issue.
B. OUR CONTRIBUTION
This work proposes a novel approach for clustering formation
and maintenance of a VANET structure in an urban scenario.
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M. K. Jabbar, H. Trabelsi: Novelty of Hypergraph Clustering Model (HGCM) for Urban Scenario in VANET
It is called the hypergraph clustering model (HGCM).The
CH stability is governed by a cumulative multimetric factor
inclusive of relative speed, eccentricity, neighbourhood and
spectrum sensing based on cooperative trust. The contribu-
tions of this work are listed below:
•As per our knowledge, this work is the first of its kind
to introduce a formulation of VANET through a hyper-
graph. The construction of the hypergraph is designed
using the distance proximity amongst the vehicles in the
network.
•Practical and optimal partitioning of the hypergraph
through tensor trace maximisation (TTM) is proposed.
A high order has all the edges but with negligible
weights. Thus, the adjacency matrix is nearly sparse,
and the overall computational complexity is effectively
reduced.
•Optimal clusters are selected in accordance with the
Calinski–Harabasz concept. This method is an external
criterion for selecting optimal clusters. Hence, the infor-
mation is independent, and the structure of the infor-
mation is inherited. Such a method is also preferred for
convex clustering.
•The network’s performance, especially in an urban
scene, can be improved by installing auxiliary facil-
ities, such as RSUs. Here, an evolving graph struc-
ture of the traffic is conceived using betweenness
centrality.
•Spectrum sensing is redesigned as a classification prob-
lem. The method proposed for sensing is long short-term
memory (LSTM), which is extensively trained for all
signal types, including noise. Thus, it can sense an
untrained signal and classify a vehicle as primary or
secondary.
•The scheme of a cumulative multimetric for selecting
a CH is presented, through which strong connectiv-
ity and stable link lifetime are maintained. The sta-
bility of the CH enhances the routing performance
of the designed approach. Extensive simulation and
comparison of the proposed scheme with existing
state-of-the-art techniques are presented to show its
supremacy.
C. PAPER ORGANISATION
This paper discusses a new hypergraph-based multimetric
CH selection algorithm that increases the CH stability. The
algorithm is tested on the Baghdad City map. The rest of this
paper is organised as follows. Section II presents a literature
review of some clustering algorithms and research problems.
The proposed hypergraph generation method is introduced
in Section III. Section IV introduces the CH selection met-
rics, cluster maintenance phase and time complexity for the
proposed method. A simulation and a comparative analy-
sis with existing state-of-the-art techniques are presented in
Section V, and concluding statements with future prospects
are provided in Section VI.
II. LITERATURE REVIEW
A. RELATED WORK
An intensive literature survey is conducted, especially on the
user information-based methods employed for clustering.
In 2001, Basu et al. [6] primarily designed the MOBIC
method for MANETs on the basis of the ratio of the power
levels received at each node from its neighbours. The authors
proposed a distributed clustering algorithm for CH selection.
The algorithm was tested on a simulated area in NS-2 but
not in an actual scenario, and the method considered only
the radio signal. Code division multiple access (CDMA) was
proposed by Kayis and Acarman [7]. It was an intervehi-
cle communication scheme, in which nodes were assigned
a specific task autonomously on the basis of their speed,
then clusters were formed. Only a theoretical approach was
projected here. Su et al. [8] designed a scheme based on a
multichannel communication with three primary protocols
for reducing data congestion, QoS and efficient bandwidth
over a vehicle-to-vehicle (V2V) network. The method pro-
posed by Rswshedh et al. [9] grouped vehicles in accordance
with mobility patterns and minimised the total number of
created clusters. Another work introduced by Maslekar et al.
[10] also reported using the location and direction of vehicles
for CH selection. Here, a direction-based clustering algorithm
was used for data dissemination. Through this approach, the
protocol density of vehicles on a given road was estimated.
A novel concept of node precedence algorithm was proposed
by Goonewardene et al. [11]. Robust mobility adaptive clus-
tering (RMAC) identified a one-hop neighbour and selected a
CH using the relative node mobility metrics of speed, location
and travel direction. An evolving structure was created via
neighbourhood analysis. With the same mobility concept,
another scheme using the affinity propagation algorithm was
proposed in a distributed manner by Shea et al. [12]. The
authors claimed the existence of clusters with high stability.
The stability of CH has been the main focus of researchers.
For instance, a multilevel clustering algorithm that mainly
concentrated on the stable, long lifetime of clusters was
designed by Vodopivec et al. [5]. The cluster formation
was based on factors, such as the density of the connection
graph, link quality and traffic conditions. Mohammad and
Michele [4] designed another method to improve cluster life-
time, especially in an urban scenario, based on the lane con-
cept. The technique was effective in reducing the overhead
of reclustering and led to an efficient hierarchical network
topology. A three-based passive clustering was introduced by
Wang and Lin [13] to improve intervehicle communication
and eventually cluster stability. The method also reported
enhanced performance in network analysis. A beacon-based
clustering algorithm was proposed by Souza et al. [14] to re-
establish cluster stability in the case of reclustering. Another
proposed method in [15] formulated a weighted approach
that included such parameters as the number of neighbours
based on dynamic transmission range, the direction of vehi-
cles, entropy and distrust value. The authors tried to increase
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M. K. Jabbar, H. Trabelsi: Novelty of Hypergraph Clustering Model (HGCM) for Urban Scenario in VANET
stability and connectivity with the reduction in overhead.
They also tested the adaptive allocation of transmission range
technique. An adaptable mobility-aware clustering algorithm
based on destination positions (AMACAD) was introduced
by Morales et al. [2]. The authors presented the concept of
adaptive mobility. Wolny [16] primarily focused on improv-
ing cluster stability by modifying the DMAC algorithm.
An adaptive service provider infrastructure (ASPIRE) archi-
tecture was designed by Koulakezian [17] by using the con-
cept of vehicular mobility in a highway scenario. The author
allowed vehicles to connect to the network through regular
mobile IP nodes, thereby increasing the connectivity and
decreasing the overhead by caching in clusters. The same
ideology of mobility was reintroduced using the concept of
multihop, and a new clustering scheme based on multihop
was presented by Zhang et al. [18]. Considering that vehicle
direction is also an important parameter, Maslekar et al. [19]
introduced the concept of CH switching. The speed difference
between neighbouring nodes was taken to obtain a stable
clustering structure [20], [21]. The interest in the multihop
approach is evident amongst researchers. The establishment
of a multihop-based clustering scheme using neighbourhood
has been exploited [22], [23]. Relevant approaches allow an
optimal set of nodes to join the same cluster and increase sta-
bility. With the advances in technology, researchers have also
proposed a complete solution for VANETs, which includes
CH selection, cluster formation and maintenance. A link
reliability-based clustering algorithm (LRCA) was designed
by Ji et al. [24] to filter out unstable neighbours on the
basis of the link knowledge providing a complete solution
of VANET. Alsuhli et al. [25] proposed another approach
called double-head clustering (DHC). This approach con-
ceived a complete solution by using metrics, such as vehi-
cle speed, position and direction, in addition to other met-
rics related to the communication link quality, such as the
link expiration time and the signal-to-noise ratio. A novel
concept of primary and secondary CHs, called enhanced
weight-based clustering algorithm (EWCA), was introduced
by Bello Tambawal et al. [26] to improve stability. Short-
range vehicle communication-based clustering in VANETs,
named centre-based secure and stable clustering (CBSC)
algorithm, was proposed by Cheng and B. Huang [27].
The literature survey comparatives based on the traffic sce-
narios, achievements, limitations, and various metrics used
for cluster formation are presented in Table 1.
B. RESEARCH PROBLEMS
This complete literature survey is for two decades, in which
the primary focus has been the stability of CH. However,
VANET clustering requires cluster generation/maintenance
and CH selection as two research areas. During the study, the
following few issues have been identified:
•The work on the real scenario is mostly limited
to the highway; analysis on the urban scenario is
missing.
•The mobility and neighbourhood are the most metrics
taken, and these metrics are lost in the urban scenario as
the vehicle speed is low and there is huge congestion in
peak hours.
•VANET is a continuously changing topology, which
creates challenges in establishing a connection from one
source to the destination vehicle. If the connection is
multihop, then the data loss can be high as the carrying
vehicle may change the direction and speed. Accord-
ingly, the information should be transmitted in a single
hop, which is feasible by making a reliable cluster. A CH
is elected amongst the neighbouring nodes. Along with
efficient cluster generation, the CH-annotated vehicle
is responsible for improving the network performance.
Sustaining a CH for a long period is difficult.
•Researchers have made clusters and selected the CH
by calculating the vehicles’ behaviour in the network,
velocity, moving direction and position in lanes. Fuzzy
logic has been used, such as in [29], [30], along with
other heuristic algorithms, such as in [33], [34]. Fuzzy
logic schemes require tuned membership functions to
decide for CH selection, which necessitate considerable
experience and behaviour analysis of vehicles on a par-
ticular road [35]. Owing to fast-changing topology and
distributed VANET architecture, heuristic algorithms
hardly make decisions due to several iterations in the
calculation. They cannot cope up with the changing
frequency of a VANET environment in a crowded city.
However, we assume that in highways with few vehicle
densities, they may present good performance.
With all these gaps in the literature studied, our primary goal
is to design a complete solution for VANET, especially for
the urban scenario. The designed approach has cluster for-
mation, CH selection and maintenance. The evolving nature
of VANETs is meritoriously captured using the concept of
hypergraphs and the clusters are formed through the designed
hypergraph algorithm. For CH selection, a cumulative mul-
timetric is designed to consider four factors: relative speed,
trust, neighbourhood and eccentricity. The trust metric is
introduced with deep learning spectrum sensing. Spectrum
sensing using LSTM is introduced. This deep learning solu-
tion enables the detection of signals. It allows effective utili-
sation of the spectrum, especially in an urban scenario where
excessive congestion occurs during peak hours. The spectrum
can be used by primary users (PUs, e.g. ambulance, police
or emergency). A cumulative multimetric maintains strong
connectivity and stable link lifetime. The proposed scheme
is tested on the real map of Baghdad.
III. PROPOSED MODEL
A multilane road structure in an urban scenario is considered.
Fluctuating density of building infrastructure and vehicular
mobility with total number of vehicles N are infused into
the real map scenario with corresponding speed and loca-
tions. This scenario is depicted in Figure 1. Each on-board
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TABLE 1. Comparative literature survey on cluster formation metrics in the existing state of the art.
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unit (OBU) equipment has the same transmission range Rvehi.
The same communication module is taken to communicate
with auxiliary facilities, each having a transmission range
RRSU . Communication amongst vehicles is carried out using
the V2V protocol. A Global Positioning System (GPS) unit
and IEEE 802.11p radio equipment are embedded inside
the OBU. By contrast, Vehicle to Infrastructure is used for
communication between vehicles and RSU. Each vehicle in
the network serves as a node (V) that performs as either
source, destination or router.
The main task of these nodes is to broadcast information
within the network. The vehicles are said to be one-hop
neighbours if the distance between them is less than Rvehi and
multihop if the distance between them is greater than Rvehi.
In this section, the formulation for designing VANET as a
hypergraph-partitioning problem is discussed in detail. The
commonly used set of notations is presented in Table 2. The
complete work can be divided into four major steps:
1. Neighbouring vehicle identification and adjacency
matrix generation
2. Hypergraph-based spectral clustering for cluster for-
mation
3. RSU deployment and cluster members (CMs) allot-
ment
4. Stable CH selection
The flow diagram of the complete work is shown in Figure 2.
The pseudo code of the suggested work is jotted down in
Algorithm 1.
A. WHY IS VANET A HYPERGRAPH NETWORK
As discussed previously, the problem of stable CH selection
to reduce the overhead and packet drop probability is twofold.
Vehicle cluster generation is not a novel but a populated con-
cept, and various scholars have already addressed it. A net-
work of vehicles is presented as a graph, in which a vehicular
node is connected with two other vehicular nodes [28], [33],
[36]. This graphical representation may be suitable in sparse
density, such as highways or minimally populated cities.
On the contrary, in dense urban scenarios, a vehicle is always
connected with more than two vehicles, and graph theory
does not fit there. Hypergraphs are a suitable representation
of dense vehicle networks. The following are the key reasons
to represent VANET as a hypergraph:
•VANET is a cooperative network where every decision
depends on the information shared by neighbouring
vehicles [37].
•In the graphical representation, a loss of information
occurs in paired connections. For tasks such as analysis
and learning, pairwise graph models lack the represen-
tational ability to adequately capture and show higher-
order information. Higher-order interactions in these
systems can be captured using hypergraphs, which show
interacting components as nodes and hyperedges.
•All vehicles in the network act as either sources, desti-
nations or routers, depending on where they are in the
Algorithm 1 Pseudo Code of the Proposed Scheme for Stable
CH Detection
Input: Vehicle-to-vehicle transmission range, RSU-to-vehicle
transmission range
1. For i=1:vehicles
a. All neighbouring vehicles within the vehicle trans-
mission range are identified
2. End for
3. Calculate the similarity matrix on the basis of the
distance proximity amongst vehicles
4. Generate an adjacency matrix
5. Create eigen values for each vehicle by using
hypergraph-based TTM
6. Apply k-mean clustering with Calinski–Harabasz for
the optimal number of clusters.
7. The centrality index gives the RSU deployment loca-
tion
8. Simulate the VANET for different vehicle densities
in the network and collect the vehicle moving angle,
locations and other information until every vehicle
leaves the network.
9. For i=1: clusters
a. For j=1: vehicles in cluster
i. Calculate the CH parameters: neighbourhood
degree, relative speed, trust score and eccen-
tricity
ii. Combine these matrices to obtain a single
score for each vehicle
iii. Highest-scorer vehicle is termed as the CH
b. End for
10. For i=1: vehicles
i. Selected CH sends frequent polling signals
ii. If ( the distance between the CH and vehicle <=
CH transmission range) then
a. The CH receive signal in return within a stip-
ulated time period
b. CH Adds the vechicle in the RSU List&CH
Local List
Else
a. The vehicle does not reply within the speculated
period time_span
b. This vehicle is considered to be disconnected and
leave the cluster
c. CH Removes the vehicle from the RSU List&CH
Local list
End if
End for
11. End for
network’s hierarchy. One of the primary responsibilities
of these nodes is to disseminate the data throughout
the network. Vehicular mobility and the communication
link amongst vehicles that is constantly breaking and
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M. K. Jabbar, H. Trabelsi: Novelty of Hypergraph Clustering Model (HGCM) for Urban Scenario in VANET
FIGURE 1. The clustering model for VANET.
FIGURE 2. Flow diagram of the proposed HGCM scheme.
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M. K. Jabbar, H. Trabelsi: Novelty of Hypergraph Clustering Model (HGCM) for Urban Scenario in VANET
TABLE 2. Frequently used notations.
reconnecting cause such networks to grow in nature.
The relationships amongst nodes in more diversified
vehicular networks are more difficult to understand
because of the networks’ ever-expanding character. As a
result, complex networks now utilise super networks.
Hypergraph-based and network-based are super net-
works that exist in the literature [37]. Hypergraphs pay
more attention to the dynamic evolution process, making
it possible to conduct a dynamic analysis of complicated
networks.
•The advantage of the hypergraph theory is that it
guarantees the homogeneity of points and edges. This
helps to express the relationship between nodes and
edges clearly. Thus, networks’ representation can be
modulated using a hypergraph, in which one vehicle can
communicate with many vehicles.
B. FORMULATION AS HYPERGRAPH PARTITIONING
A connected weighted hypergraph is a three-tuple of H=
(V,E,W), where each edge Elinks a subset of vertices Vin
the hypergraph and may be linked with non-negative weight.
This structure is composed of n vertices, V= {vi|i=
1,2, . . . n}, where each vertex is a vehicle in our study, E=
cij : {<vi,vj>|vi∈VVvj∈VV(dij≤Rvehi }is an
edge set, and W→[0,1]is the weight associated with each
edge. The distance of each vehicle constitutes the edge of
each hyperconnection. The hyperedge connection is defined
in Definition 1.
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Definition 1: Two vehicular nodes viand vjat time t are
said to be connected if
cij =(1dij ≤Rvehi
0dij >Rvehi
(1)
The connection between two vehicles is established using
the distance proximity formulation. Here, the connection
is established if the distance between the two vehicles
dij is less than the transmission range of the vehicle
nodes.
Using the existence or weight of edges, we want to divide
V into k disjoint sets (V1,...,Vk). The related weights for
m-uniform hypergraphs are archetypally called m-way affini-
ties as each edge has distinct m vertices.
C. HGCM GENERATION MODEL
The cluster generation part of VANETs is discussed in
this section. An urban scenario is considered for the sim-
ulation, and location information is shared with every
neighbouring vehicle in the test case. A network hyper-
graph is constructed using that location information, and
this section discusses the formulation of the vehicle
hypergraph.
Our proposed model aims to cluster vehicles so that
minimum bandwidth occupancy at any instant is achieved
[38]. In the urban scenario, road congestion is unavoid-
able, leading to slow-moving traffic. The location, speed
and vehicles in an area affect the stability of the cluster-
ing [39]. Each vehicle in a cluster is categorised as either
CH or CM. Only one CH is conventionally allowed in
a cluster, except in special cases of warlike fields [40].
In this article, the maximum possible vehicle density Nis
considered for the clustering algorithm. Using the location
information, each vehicle finds its neighbour. A similarity
matrix is generated, whose cell elements indicate the connec-
tion strength with another corresponding vehicle, as shown
in Figure 3.
The adjacency matrix showcases the relation amongst the
vehicle nodes. Spectral clustering using TTM is introduced
in this subsection. The problem is partitioning the weighted
hypergraph Vinto kdisjoint sets, V1,......Vk, such that
the total weight of edges within each cluster is high (dense
connectivity amongst the vehicles), and the partitions are
balanced [41]. The number of vehicular nodes connected to a
node is defined as the degree of any node, v∈V, defining
the total weight of edges vthat is incident, i.e. deg (v)=
Pe∈E:v∈ewe.
Next, the volume is defined as CM (V1)=PvV1deg(v),
which is the number of nodes incident on node V1, such
that V1⊆V. The association amongst the edges contained
within V1is defined as assoc(V1)=Pwe. The normalised
associativity of these individual partitions is given as
Par (V1,......Vk)=Xk
i=1
assoc(Vi)
CM(Vi)(2)
The adjacency matrix defined here is of the tensor (order z),
Ai1,i2,......iz=(w{i1,i2........ iz}if i1,i2,.........,izare distinct
0otherwise
(3)
The normalised associativity can be rewritten in terms of A
and Y(inverse of the number of vehicles connected to a node)
as
Pari∈{1,..k}
=1
z!Trace(A×1Y(1)T×2Y(2)T×3Y(3)T.......×zY(z)T)
(4)
where ×lis the model-l product.
Y(1)T,Y(2)T,Y(3)T. . . . . . ., Y(z)T∈Rk×z, which repre-
sents the number of CMs connected to each node vifor each
vertex. Yi∈{1,2..z}, as shown as follows:
Yi=1
PkCM(Vi)(5)
The designed adjacency matrix [42] is considered for spec-
tral clustering, and this hypergraph is now transverse to obtain
the diagonal matrix (degree matrix) Dig that is the sum of runs
over all the vehicle nodes that are one-hop adjacent to node vi.
Digii =XN
j=1Aij (6)
For the Laplacian graph computation, this study utilises the
unnormalised Laplacian matrix based on the Fiedler vector
defined as
L=Dig−1/2ADig−1/2(7)
The top keigenvector (X=eig(L)) is taken for k-means clus-
tering that provides k–partitions of the VANET hypergraph
structure. These partitions resemble the cluster formation in
the vehicular network. They are further pruned to generate the
optimal set of clusters for VANET maintenance. The pseu-
docode for the spectral clustering is listed in Algorithm 2.
Definition 2: The weighted hypergraph H=(V,E,W),
and its cluster is a tuple of (Cnum,Coptimal), where Cnum =
{ci|i=1,2, . . . ..k}is a cluster set, where kis the total number
of clusters. ∀ci∈Cnum,ci= {vj|τ τ vj=0∨(τvj=
1∧ ∃vk∈Nvj∧τ(vk)=0)}.
Coptimal represents the optimal set of clusters, Coptimal =
[Cnum : ∀max (s)].
The clustering efficiency can be evaluated using the
Calinski–Harabasz index (s) [43]. This index checks the
closeness of vehicles in a cluster and the dispersion of all
clusters by using Equation (8). The maximum value of s is
the desired efficiency in the clustering.
s=tr(Bk)
tr(Zk)×Vehinum −k
k−1(8)
Here, krepresents the number of clusters, and each has the
size of Vehinum .tr(Bk) is the dispersion amongst clusters, and
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M. K. Jabbar, H. Trabelsi: Novelty of Hypergraph Clustering Model (HGCM) for Urban Scenario in VANET
FIGURE 3. Hypergraph based VANET analysis.
tr(zk) is the dispersion amongst vehicles in a cluster. These
two terms are calculated in Equations (9) and (10).
Zk=Xk
q=1Xx∈Cq
(x−cq)(x−cq)T(9)
Bk=Xk
q=1nq(cq−cE)(cq−cE)T(10)
Here, cqis a set of points in cluster q, and cqis specifically
the centre of the cluster. cEis the centre of clusters with nq
points in them.
With the help of this index, an optimal set of clusters from
the pool of formed clusters is selected on the basis of the
maximum value of s.
D. RSUS DEPLOYMENT
The RSU is an integral part of the VANET. The VANET
is a hierarchical architecture consisting of the main server,
RSUs, and vehicles. RSU collects the data from the moving
vehicles. The clustering of vehicles has been discussed in
the context of RSU by many researchers as if the RSU has
request congestion, then packet drop will increase. Therefore,
the optimal number of RSUs has to be calculated so that
maximum probable vehicles can be served without conges-
tion. The optimal number of clusters has been calculated
in the previous section. The RSU is placed at the centroid
of the cluster. This way, a minimum number of RSUs can
cover the maximum number of vehicles in the area. The
installation cost would also be lesser (this is not evaluated
in the simulation). Algorithm 3 tabulates the steps in locating
the centroid for the RSUs and their deployment. The vehicles
in any cluster cannot be controlled due to the nature of
clustering. Consequently, few vehicles, such as three, can also
lie in that precalculated cluster area. In such a case, the RSU
is placed using a Gaussian probability distribution [44] as:
Vehi ∼N(µ, σ 2) (11)
Algorithm 2 Cluster Formation Using Hypergraph Theory
Input: Slot with maximum vehicles: N, Location of each
vehicle: VehiLoc
1. Select the time slot twhen maximum vehicles are
present N
2. Form a hypergraph H=(V,E,W)
3. Calculate the similarity matrix Aon the basis of the
distance proximity amongst the vehicles
A square matrix of size N×Nof similarity (adjacency
matrix) as A=PN
i3,.....,iN=1Aij
4. A diagonal matrix Dig ∈RN×Nis with Digii =
PN
j=1Aij, and L=Dig−1/2ADig−1/2
5. Then, kdominant eigenvector of Lis computed as X∈
RN×k
6. Normalise each row of ¯
X=X
7. Run k-means on the rows of ¯
X
8. Obtain Cnum through k-means partition Par =
{V1,......Vk}
9. For each cluster Cnum, calculate the Calinski–Harabasz
(s) criterion
10. Find the optimal cluster Coptimal =[Cnum : ∀max (s)]
Output: The optimal set of clusters: Coptimal
The distribution is defined as the mean (µ=0) and variance
σ=1.
f(Vehi)=1
σ√2πe−(Vehi−µ)2/2σ2(12)
A network graph G =(V,E) amongst V vehicles’ con-
nections with εset of edges. The centrality matrix for a
graph is the measure of its compactness [45]. The centrality
determines the most visited vertex in a graph. For a vehicle v,
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it can be calculated as
CB(v)=Xs6=v6=u∈V
σst (v)
σst
(13)
Here, σst is the total number of the shortest paths from nodes
to node u, and σst (v) is the number of paths that pass through
v. The vehicle with maximum centrality value is considered
the cluster’s centre as in (line 10). This is the location where
RSU is to be installed.
Algorithm 3 RSU Deployment
Input: Set of optimal clusters Coptimal and number of vehicles
in each cluster Vehinum .
1. For i=1: Coptimal
2. If Vehinum <3
3. Select a vehicle based Vehi ∼N(0,1) shown in
Equation (12)
4. RSULoc =VehiLoc
5. Else
6. Construct an urban road map with a graph G=
(V,E)
7. Edge is eijE=dij based on the distance
amongst vehicles
8. Obtain a connection matrix
cij =(1if dij ≤Rvehi
0otherwise
9. Evaluate the betweenness centrality CBby
using Equation (13)
10. Vehi =max(CB)
11. RSULoc =VehiLoc
12. End
13. End
Output:RSU location RSULoc.
IV. CH SELECTION AND CLUSTER MAINTENANCE FOR
HGCM
A. CH SELECTION
The vehicle node viin the network at time thas features
fi(t)= {Es,Ep,a, ϕ, VehiID, η}, where Es is the vehicle speed,
Ep is the location of each vehicle in both coordinates (x,y),a
is the acceleration, and ϕis the vehicle direction. Each vehicle
is assigned a unique identity VehiID , and ηrefers to the
one-hop neighbours of vehicle node vi. Out of these nodes,
a vehicle is selected as the CH. In this article, the CH selection
metric mi(t)is a collection of metrics {ψvehi, η, E,t}. The CH
selection process is dependent upon the current CH selection
metrics of each CM in the cluster. ψvehi is the relative speed,
ηis the set of neighbours of vehiclevi,Eis the eccentricity,
and tis the trust calculated via spectrum sensing. The selected
CH should have a maximum of Pi=1,2..nmi(t)at any instant
t. Given that the hypergraph network is the cooperative net-
work, each vehicle’s feature is relative to every hyperedge
linked to that hypernode [46].
The novel contribution in CH selection parameters is the
strength of the cooperative nature of the hypergraph. The use
of deep learning in the calculation of the trust score of each
vehicle is another novel contribution to the CH selection.
The CH collects all the information from the network,
sends it to the RSU and maintains the communication
between the cluster vehicles and RSU. The stability of the
CH will be higher if it will be in a communication link with
the neighbour vehicles for a longer time.
The definitions of each metric with the essential back-
ground are presented below.
1) RELATIVE SPEED SCORE (ψvehi )
Definition 3: A vehicular node’s vjrelative speed score
ψvehi is a score that either penalises or gives reward to a
vehicle if it crosses a cluster’s average speed or aligns with
the cluster. A high score of ψvehi indicates a high probability
of election.
This parameter determines how close a vehicle’s speed is
to its neighbour’s. The relative speed of each vehicle is cal-
culated by differentiating its speed from the cluster’s average
speed at any instant of time. The moving direction of the
vehicles also comes into play this way. The more vehicles
are moving in the same direction, the higher ψvehi will be. the
relative speed score is evaluated as shown in equation (14)
[21]. The relative speed is compared with a threshold speed
sthr . If a vehicle is moving at higher speed than sthr , its ψvehi
gets penalised with δ; else, a reward of δis added to its score.
ψvehi (t+1)=ψvehi (t)+δ;Vvehi −Vavg≤Sthr
ψvehi (t+1)=ψvehi (t)−δ;Vvehi −Vavg>Sthr
(14)
δand Sthr are 0.01 and 2.77 for this work, respectively.
2) NEIGHBOURHOOD DEGREE (η)
Definition 4: The connection status between the two vehic-
ular nodes viand vjat time t in the cluster formed coptimal with
vehicle density vehinum is defined as
η=XVehinum
j=1cij; ∀1 (15)
High ηensures that the CH will not be dynamic for a long
time. The neighbourhood degree defines the total number of
vehicles in the vicinity. The vehicles under the transmission
range of OBU are considered neighbours. cij is 1 if the
distance between two vehicles at the time stamp t is less than
Rvehi [47]. A negative correlation exists between the distance
and transmission range. That is, if two vehicles are close to
each other, then a more reliable connection is bound.
3) ECCENTRICITY (E)
Definition 5: Let Abe a fundamental matrix. Then,
an eigenvector X>0 exists, such that AX =λ1X, λ1>0 is
an eigenvalue of an immense magnitude of A, the eigenspace
associated with λ1is one-dimensional, and X is the only
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non-negative eigenvector of A.Eis the average of top k
eigenvalues of Adesigned for H=(V,E,).
In real time, communication links break frequently due to
vehicles’ high speed. to maintain a link, a requisite is set for a
progressing cluster model. Usually, reclustering will become
inevitable once the CH resigns or loses its suitability to con-
tinue as a CH. to ensure stability, the concept of eccentricity
(E) is introduced. Here, an evolving graph-based model is
designed through spectral clustering [28]. A vehicular graph
topology is intended to be hypergraph H=(V,E,W)with
the usual procedure as defined in section III. the adjacency
matrix Ais generated on the basis of the distance proxim-
ity amongst the vehicles present at each time instant t for
each cluster. The eigenvalues for a vehicle iin each group
are λi, where i={1,2,......vehinum}. Lastly, Eis the
mean/average eigenscore of each vehicle calculated as [28]
E=1
|Vehinum |XλiVehinum
λi(16)
The maximum value of Eensures a stable CH selection
designed in accordance with hypergraph theory.
4) TRUST SCORE (t)
Definition 6: Through channel h, the signal is received
from the user, and the probability of detection is 1. Then, the
user is primary (PU); else, it is a secondary user (SU).
The vehicular network may also have some VIP and emer-
gency vehicles, which are regarded as the PUs of the commu-
nication spectrum in the network. Others are assigned as SUs.
Every vehicle takes part in spectrum sensing. Given that the
communication spectrum is limited, the cognitive spectrum
sensing approach is used in the communication model [48].
Once the PU is detected in the network, the SU will have to
vacate the spectrum for it. The SU following this protocol
gains the trust, and the trust score tis increased. The model
of cognitive spectrum sensing is introduced in this work to
select the most trustworthy vehicle as the CH.
The SU senses the PU presence by comparing the signal
energy of neighbouring vehicles with the probabilistic thresh-
old value. The detected energy signal (test statistic) can be
presented in a complex form as
T(Y)=1
2NXN
i=1Yre
i+Yim
i
2(17)
where T(Y) is the test statistics received on any vehicle. This
T(Y) is a random variable and can be estimated using the chi-
square probability distribution function as
Pd(ε, t)=Q ε
σ2
u−γ−1stfs
2γ+1!(18)
The vehicle is detected as the PU if the probability of detec-
tion Pdis greater than threshold ε[49]. εis calculated by the
inverse of this chi-pdf:
Q−1(Pd)=ε
σ2
u−γ−1stfs
2γ+1(19)
Here, Q(.) is the complementary distribution function and is
Gaussian in nature, i.e.
Q(x)=1
√2πZ∞
x
exp(−t2
2)dt (20)
The threshold value decides the accuracy of detection of the
PU. In this work, we follow the concept of deep learning
to detect the presence of PU. It has proposed the stack of
deep learning layers with LSTM in the focus to factor down
the signal features. Threshold value estimate is comprised of
two distinct stages: data generation and deep learning model
training.
The spectrum sensing network is simulated in ideal condi-
tions to generate the training data with various modulation
schemes and random input data streams. Simulated modu-
lations are BPSK, QPSK, 8-PSK and 16-PSK. With every
simulation, the generated signals’ energy is mapped with the
results of the PU detection with a threshold value calculated
using Equation (17). As a result, forty thousand samples are
used to create a labeled dataset. The PU and non-PU labels
are assigned to detected signals.
The LSTM network is trained on the data to teach the deci-
sion based on sensed signal energy. The network is trained
with the randomly sampled 90% data for training and 10% for
the testing. Two biLSTM layers with forward and backward
data sequencing are used which are connected with the fully
connected layer. On training, the network is able to correctly
classify the absence of any PU upto 89% whereas any PU is
correctly detected upto 83.5%.
The trained network is used to obtain the threshold value
for Pd(ε, t)on the unknown signals. For every successful
detection, the trust score (t) is incremented. The higher tis,
the higher the probability of a vehicle to be elected as CH
will be. This trust score calculation scheme is portrayed in
Figure 4.
The model is divided into three subparts: sensing block,
training block and PU detection block. The energy signal
database is collected by simulating the network in the ideal
and Rayleigh noisy channel environment. The data are fed
into the LSTM training block. After training, the detected
energy signal is tested with the trained model, and the vehicle
is assigned to the PU or SU. The true detection increases the
trust score by 1.
A comparison of the ROC curve between the theoreti-
cal analysis of threshold calculation by Equation (19) as in
[50] and the proposed LSTM-trained network is presented
in Figure 5. The detection probability Pdis high for a small
value of Pf. The trained LSTM network performs better in a
noisy environment, which means that it is efficient and can
predict with appropriate accuracy.
The complete algorithm designed for CH selection is
shown in Algorithm 4. All four parameters are summed and
integrated to select a stable CH for a long period of time.
The vehicles are firstly clustered using Algorithm 2. For all
members at each cluster, the four parameters are found. Then,
CHscore is calculated to select the stable CH.
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FIGURE 4. Adaptive spectrum sensing model using LSTM.
FIGURE 5. The Pdand Pfusing LSTM method and theoretical analysis.
B. HGCM MAINTENANCE PHASE
The reduction of communication overhead after the selection
of CH is also an important part of the designed algorithm.
The cluster maintenance process ensures strong connectivity
and stable link lifetime through CH. In this work, the joining
of a new vehicle in a cluster and leaving of any CM are
considered vital for the cluster maintenance phase. HGCM is
designed with the parameters that ingest the restructuration
of the topology and vehicular speed. The CH score provides
a significant contribution to capturing the information of
vehicle movement. The maintenance does not deal with the
networking. It is designed to maintain a smooth transition of
vehicles in and out over time.
1) CLUSTER ENROLMENT
Cluster formation is performed on the basis of the proxim-
ity of vehicles concerning the transmission range of RSU
Algorithm 4 CH Selection
Input: Relative speed Vvehi and location
[x,y];Number of lanes in a map (no_lane);time_span;
Cluster member (CM); (N) no. of clusters.
1. For t=1:time_span
2. For i=1:N
3. For j=1:CM
4. Calculate ψvehi from Equation (14)
5. Find the neighbouring vehicles and calculate ηby using
a connection matrix Equation (15)
6. Calculate the maximum eigenvalues λ;
7. Then obtain Eby using Equation (16)
8. Signals’ energy is mapped with the results of the PU
detection with a threshold value calculated using Equa-
tion (17) and Equation (19).
9. Calculate tscore using the LSTM trained network
based on sensed signal energy.
10. Find CHscore for each CM
11. CHscore =ψvehi +η+E+t
12. End
13. CHj=Max Pk
j=1CHscore∀j
14. End
15. End
Output: CH
deployed. A small number of vehicles in a cluster with a
large transmission range will lead to inconsiderably reliable
networking. The selected CH starts its task by sending the
polling signals and if it receives any signal in return within
a stipulated time period time_span with the condition that
dist_(vehi,ch)<rch. A new vehicle is assigned to that cluster
(each formed under RSU) and becomes CM of that particular
cluster. CH will update the local database and the list of
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vehicles in RSU. The arrival of a new vehicle in a cluster
can also trigger CH reselection in the worst-case scenario.
The algorithm designed is thus coined to formulate CH score
based on four factors {ψvehi, η, t,E}; with this, the stability
of CH is ensured.
2) CLUSTER LEAVING
CMs can leave any cluster at any moment of time. The reasons
for this could be lane change or exit from a road, the ever-
changing dynamics of vehicles and the topology that affects
the number of CMs. Therefore, a frequent polling of signals
is done between the established members and CH. If a CM
does not reply within the speculated period time_span, then
the CM is considered to be disconnected and leave the cluster.
The CH removes the recorded vehicle, and an updated list is
appended at the RSU. The complete algorithm designed for
cluster maintenance is shown in Algorithm 5.
Algorithm 5 Cluster Maintenance
Input: CH; Cluster C;No. of vehicles N ;CH transmission
range RCH
1. For t=1:time_span
2. For j=1:C
3. For i=1:N
4. IF dist_(vehi,CH)<RCH
5. CM=CM+1;
6. CH <Adds the vehicle in the RSU List&LocalList >
7. Else
8. CM=CM-1
9. CH <Removes the vehicle from the RSU List &
LocalList >
10. End
11. End
12. End
13. End
Output: Cluster Update
3) TIME COMPLEXITY OF THE HGCM SCHEME
Cluster formation, RSU deployment and CH selection are the
key components of the proposed algorithm. Accordingly, the
algorithm’s total time complexity is expressed as
OTOT =OCF +ORSU +OCH (21)
where OCF is the time complexity of cluster formation, ORSU
is for RSU deployment, and OCH is for CH selection. The
cluster is generated by hypergraph partitioning. The major
steps involved are as follows: (1) hypergraph construction=
(V,E,W); (2) Laplacian construction; (3) eigen problem
solving; (4) vertex eigenvector computation; (5) performing
k-means on ¯
X.
In a hypergraph with pairwise similarity, the cost to con-
struct the nearest neighbour graph is ON2d, given that
it requires d-dimensional similarity computation for each
vertex pair, where Nis the maximum number of vehicles in
the worst-case analysis with mhyperedges. The Laplacian
construction step is directly correlated with the sparsity of
adjacency matrix Athrough the non-zero elements NNZ (or
the number of vehicles in our case). L=NNZ(A2), the
eigen complexity is EC=O(N3), and the last is the k-means
complexity which is dependent on OCoptimal =τNCnum, where
τis the number of iterations.
OCF =ON2d+NNZ A2+ON3+τNCnum
(22)
This can be reduced after removing the terms of less compu-
tational power as
OCF =ON2d+ON3(23)
The RSU deployment is done using a graph, so the computa-
tional complexity is
ORSU =ON2d(24)
In this article, the CH selection metric mi(t)is a collection of
metrics {ψvehi, η, E,t}.ψvehi is the relative speed, ηis the set
of neighbours of vehicle vi,Eis the eccentricity, and tis the
trust calculated via spectrum sensing
OCH =Oψvehi +Oη+OE+Ot(25)
The relative speed is a simple threshold function done on the
basis of the vehicle speed; thus,
Oψvehi =N(26)
The next is the neighbourhood, which is a function of the cij
affinity matrix for nearby vehicles.
Oη=O{log N2}(27)
The eccentricity is calculated using spectral clustering meth-
ods that include the affinity matrix and eigenvalue decompo-
sition. The entire spectral clustering complexity is
OE=OnN2od+O{N3}(28)
The last factor is trust LSTM, which plays the primary role
in this for spectrum sensing; the theoretical time complexity
of the LSTM is given as
OLSTM =4IH +4H2+3H+HK (29)
where Irepresents the number of inputs, Krepresents the
number of outputs, and Hrepresents the number of hidden
layers. In this study, because the model is trained only once
for a given vehicle signal, the LSTM detects whether the
vehicle is a primary or secondary user through spectrum
sensing. Thus, the time complexity condenses to
OLSTM =O{4H2}(30)
Then, the complete time complexity is reduced to moving
all the terms with less complexity than cubic and quadratic
terms, as shown below:
OCH =Onlog N2o+O{N3}(31)
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TABLE 3. Simulation parameters.
The overall complexity is primarily dependent on the hyper-
graph, i.e.
OTOT =2ON2d+Onlog N2o+2O{N3}(32)
V. SIMULATION AND PERFORMANCE EVALUATION
This section describes the detailed background of the sim-
ulation tools and the various evaluation parameters utilised.
The results’ discussion is carried out in three phases: the
effect of different traffic densities on the stability of the
designed HGCM, state-of-the-art comparison, and the effect
of different traffic densities on the routing performance in
comparison with various existing algorithms.
A. SIMULATION TOOLS
The simulation is implemented using MATLAB (R2018b),
with the processor Intel R
Core TM i7, 1.98 GHz, Simulation
of Urban Mobility [51] (SUMO 1.7.0) and Traffic Control
Interface (TraCI) [52]. SUMO is an open-source microscopic
road traffic simulator licensed under the General Public
License. It was developed through collaboration between the
Centre for Applied Informatics, Cologne (ZAIK) and the
Institute of Transportation Systems at the German Aerospace
Center (DLR). TraCI is an API developed to interface SUMO
with other coding platforms, such as MATLAB, Python and
Java. The complete network design and the routing perfor-
mance for metrics, such as throughput and PD are evaluated
in MATLAB. The area considered for the study is a crowded
market area of Baghdad having the latitude =33.3573◦S,
33.3730◦N and longitude=44.3960◦W, 44.4190◦E; it is
extracted from Open Street Map. The latitudes and longitudes
make a simulation area of size 1000 ∗2000 m2. Baghdad is
the capital of Iraq and one of the largest cities in the Arab
world, with massive population and a geographical area of
204 km2. The traffic environment summary is provided in
Table 3. These parameters are considered on the basis of
extensive literature survey. Moreover, the values are minutely
crafted to portray a real urban scenario with congestion,
many crossroads and a large number of vehicles during peak
hours [53].
The geographical region considered for the simulation is
shown in Figure 6; it is a vast area with urban infrastructure.
Algorithm 2 suggests the optimal number of clusters in that
FIGURE 6. Simulated part of Baghdad real map in SUMO.
FIGURE 7. Cluster formation along with RSU deployment at an instant
with maximum vehicular density.
region, and RSUs are deployed using Algorithm 2. Further
vehicle features fi(t)= {Es,Ep,a, ϕ, vehiid , η} are recorded for
1000 vehicles. The number of vehicles in the simulation area
varies as in real-world scenarios. Twelve clusters are opti-
mally selected using Algorithm 2. Different colours portray
each cluster and vehicles in each cluster. The triangles (in
black) are the different RSUs placed, which will serve as the
cluster centre (providing auxiliary facilities), Figure 7.
B. EVALUATION METRICS
The designed HGCM is also tested in terms of routing per-
formance. The communication amongst vehicles is modelled
through the Rayleigh fading channel with BPSK modulation.
Owing to the vehicles’ movement, the network is dynamic
and fast, which introduces a Doppler effect. The effect is
incorporated as the signal fades over time. The communica-
tion network parameters are listed in Table 4 [53].
Different metrics are calculated to evaluate the stability and
performance of our HGCM. These metrics are as follows:
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TABLE 4. Integrated network parameters for IEEE 802.11p.
1. Cluster number: It is the number of clusters con-
structed during network operation. Few cluster num-
bers enhance the clustering algorithm efficiency [54].
2. CH Stability: CH stability is evaluated as the most
prolonged interval to be crowned as CH. Mode is a
statistical function that gives the interval counts for a
vehicle as CH.
CH Stability =Mode(Xt
i=1VehiID ) (33)
3. CM Lifetime: It is the time interval from a vehicle
joining a cluster to leaving it or changing its state to
a CH.
4. CH Change Rate: It is the average number of CH
changes per unit time. A stable cluster should have
lower CH change rate.
5. Packet delay (PD): It is the time taken for a packet to
be sent from the source to the destination vehicle. The
delay in packet delivery depends on the noise, network
congestion and hop travel distance. It is measured in
seconds [54].
PD =XN
i=1(Time a packet is received
−Time a packet is transmitted)
/Number of packets (34)
6. Throughput: It is the number of bits successfully trans-
mitted from the source to the destination vehicle at a
given time period. It is measured in kilobits per second.
High throughput can be achieved with high network
stability and minimal hop count [54].
Throughput =(Packets Received ×Packet size)
/Total Time (35)
C. RESULTS AN D DISCUSSION
The designed HGCM is analysed on a real map in an urban
scenario where different densities of vehicles at various
mobilities are infused into the network. The number of clus-
ters produced throughout time affects algorithm efficiency as
well. In comparison with roads, mobility is less of an issue
in cities. CH is also more stable in an urban setting, where
the vehicle density is higher, but the mobility is lower. The
results’ discussion in this section is parallel with the state-of-
the-art schemes.
1) EFFECT OF DIFFERENT TRAFFIC DENSITIES ON HGCM
STABILITY
The work presented in [37] by Maoli et al. opened up
a way to present VANET as a hypergraph, although the
authors discussed that in the context of fog computing
and left the discussion gap on the network performance
parameters.
The effectiveness of the designed algorithm was also gazed
by the number of clusters formed over time. These numbers
allow us to evaluate the quality of the formed clusters. Few
clusters with vehicles having low mobility achieve efficient
connection and stable clustering. On the contrary, more clus-
ters eventually lead to high overhead and mergers. The aver-
age number of vehicles in a cluster represents the cluster
size. The larger the cluster size is, the higher the clustering
efficiency will be. Figure 8, shows the average number of
vehicles in a cluster and the number of clusters generated at
different vehicular densities for our HGCM.
In HGCM, four and 12 clusters are generated with an
average of 25 and 210 vehicles in a cluster at low and high
traffic, respectively.
For spectral clustering, this study employs the eigenvalues
derived using VANET’s hypergraph presentation. The idea
is motivated by the connectivity graph eigenvalues in [28]
and [33]. Both works in [28] and [33] were designed for
the highway scenario, whereas our work is designed for the
urban environment. The eccentricity parameter in our work
is inspired by the connectivity-based CH selection in [28].
A high connectivity with vehicles represents that dense traffic
and maximum CH can be connected with the maximum num-
ber of vehicles. Eccentricity is a positional parameter that can
be correlated with the connectivity issue. In a graph network,
the central point has the highest connectivity, as does in the
hypergraph. The neighbourhood degree is another connec-
tivity parameter. In CH selection, a relative vehicle speed
denotes uniform cluster generation. The CH stability using
these three parameters {ψvehi, η, E}is evaluated on differ-
ent vehicle densities in the same network and represented
in Figure 9. Given that the vehicle deployment and move-
ment are random and near to a real environment in SUMO,
{ψvehi, η, E}parameters are not able to conclude any concrete
pattern. We hereby use a nontrivial CH selection parameter,
i.e. trust score t. The trust score t, along with the remaining
three CH selection parameters, improves CH stability. The
novel set of CH selection parameters significantly improves
the CH stability by 20% at all vehicle densities as shown in
Figure 9.
Regardless of the non-uniform pattern in improving sta-
bility by the proposed set of parameters, the novel contri-
bution shows a constant improvement compared with each
parameter, as shown in Figure 10. The method designed using
eccentricity only provides satisfactory stability compared
with the others. This is because the network has a dynamic
structure that is perfectly emulated utilising the hypergraph
concept. By contrast, the rest of the parameters, such as the
relative speed and neighbours, could not trace the stability
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FIGURE 8. Av. number of vehicles in a cluster and cluster number of HGCM at different vehicle densities.
with increasing vehicle densities. The contribution of each at
an individual level is low, but the stability provided is best
when they are combined {ψvehi, η, E,t}.
The efficient cluster generation in the proposed scheme
leads to enhanced CH stability. The CH stability has
already been validated in Figure 9 and 10. The pro-
posed HGCM with CH selection parameters achieves 72%
and 53% of stability for low and high traffic density
respectively.
The CH achieves enhanced stability, as evaluated in
Figure 10. However, other vehicles in the cluster are marked
as CMs. The increased lifetime of CMs indicates efficient
clustering by using a hypergraph. In the case of non-uniform
clustering, a CM leaves clusters frequently and joins oth-
ers. In such a scenario, CH stability cannot be achieved.
Figure 11 presents a comparison of CM lifetime of our pro-
posed HGCM. The HGCM scheme gains the highest life-
time compared with its counterparts, although the traffic
congestion with the increase in vehicle’ density imposes
performance degradation. Nevertheless, it can be ignored
because for a 10-fold increase in traffic from 100 vehicles
to 1000 vehicles in the network, the CM lifetime decreases to
4.2% only.
Also, the lower change rate of the CH, the more stable the
cluster structure. From Figure 12 we can see, that the CH
change rate is the lowest due to hypergraph spectral clustered
network with the CH selected considering the four selection
metrics {ψvehi, η, E,t}.
The cumulative multimeric reduces the overhead that
occurs due to the frequent shifting of the CH from one vehicle
to another. Thus, it improves CH stability and CM lifetime
and reduces CH change rate in a comparison with individual
metrics.
2) STATE-OF-THE-ART COMPARISON
A comparison of HGCM with some algorithms presented in
the literature in terms of cluster number and CH stability is
tabulated in Table 5.
Cluster-based VANET oriented Evolving Graph (CVoEG)
[28] was introduced by Khan et al. They used a graph spectral
clustering algorithm and tested it on a highway network.
CVoEG [28] forms 20 clusters under a low traffic density,
covering a road length of 12 km under the i-5 highway anal-
ysis of the California environment. It is expected to achieve
65.5% stability. In this study, the speed of vehicles is used
to emulate graph edges. Thus, at low variance, as the speed
of vehicles is nearly identical, the eigenvalues are almost the
same, which eventually leads to low cluster formation.
Another work was presented by Khan et al. in [33]; it is
the nearest peer to our work in this paper. The authors used
connectivity-based CH selection and calculated the eccen-
tricity for it. The highest eccentric vehicle in a cluster was
assigned as the CH. In HGCM, the CH selection depends
on a novel set of vehicle parameters. RSUs are installed
at equal distances, and dynamic clusters are formed with
traffic density. A 2 km road was simulated in SUMO by
Khan et al. [33]. A maximum of 140 clusters was generated
for high traffic and 20 for low traffic in 400-s simulation.
The massive clusters in the network reduce the CH stability,
as discussed previously in this section. The authors in [33]
did not evaluate the CH stability, such that Table 5 lacks
that.
In the article proposed by M. Mukhtaruzzama [55], clusters
were generated by considering the moving direction of a vehi-
cle at the junctions, vehicles’ density, and transmission range.
The CH was selected by relative position and time spent on
the road. With 100 vehicles as a testbed, the CH stability was
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M. K. Jabbar, H. Trabelsi: Novelty of Hypergraph Clustering Model (HGCM) for Urban Scenario in VANET
FIGURE 9. Average stability of CH for HGCM with and without trust factor.
FIGURE 10. Stability of CH at different vehicle densities.
found to be 76% with a formation of 16 clusters. By contrast,
the HGCM system suggested in our work procures 72% with
4 clusters.
In the method proposed by Arkian et al. [21], a high
number of dynamic clusters are projected with a low
variance of 90 vehicles only for a highway length of
3000 m with two-lane analysis. This method incorpo-
rates neighbourhood analysis; thus, when only 90 vehi-
cles exist, to cover all vehicles in a sparse area, the
number of clusters is bound to be high. for the low traffic
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M. K. Jabbar, H. Trabelsi: Novelty of Hypergraph Clustering Model (HGCM) for Urban Scenario in VANET
FIGURE 11. CM lifetime at different vehicle densities.
FIGURE 12. CH change rate at different vehicle densities.
flow with a high number of clusters, the CH stability
is 58%.
Although the CH stability of the method proposed by
Mukhtaruzzaman et al. [55] is 76%, we can conclude that
our HGCM using hypergraph theory improves the clustering
efficiency compared with other algorithms in terms of the
number of clusters constructed with 72% of CH stability. The
CH stability for the maximum number of clusters formed is
reported in Table 5.
The graph in Figure 13 is plotted for the CH stability
for various vehicle densities. The CH stability decreases
with the increase of traffic density. On the same network
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M. K. Jabbar, H. Trabelsi: Novelty of Hypergraph Clustering Model (HGCM) for Urban Scenario in VANET
FIGURE 13. Stability of CH at different vehicle densities.
FIGURE 14. Analysis of PD and Hop distance at different vehicle densities.
TABLE 5. Comparison with different algorithms at low traffic density.
conditions listed in Tables 3 and 4, the CH stability is also
evaluated using the algorithms in articles [28], [21], and [47],
with the same vehicle properties recorded from SUMO as
for the proposed work. In Figure 13, CVoEG [28] seems
to select a lesser durable CH than the proposed HGCM,
followed by the method proposed by Arkian et al. [21] at
low traffic (100–500 vehicles) and by Kakkasageri et al.
[47] at high traffic (600–1000 vehicles). The reason is that
the ch selection in Arkian et al.’s method [21] is based on
vehicle speed. As we have mentioned previously, the speed
metric is lost in an urban scenario when there is immense
congestion. hence, this proposed method achieves the lowest
stability. HGCM achieves good CH stability in comparison
with other algorithms due to the effectiveness of hypergraph
theory and the novel set of CH selection parameters. our hgcm
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M. K. Jabbar, H. Trabelsi: Novelty of Hypergraph Clustering Model (HGCM) for Urban Scenario in VANET
FIGURE 15. Throughput at different vehicle densities.
succeeds in achieving more than 53% of CH stability from
the total time at all vehicle densities. Thus, the presentation
of VANET as a hypergraph with its eigenvalues improves the
CH stability.
3) EFFECT OF DIFFERENT TRAFFIC DENSITIES ON ROUTING
PERFORMANCE
The stable CH improves the routing parameters, such as PD
and throughput. These parameters are distance dependent.
The minimum distance travelled by the packet leads to low
PD and high throughput. All CMs should be one hop away
from the CH. In an efficient cluster, the hop distance would be
minimal. In the work presented in this paper, HGCM divides
the network into 12 efficient clusters, which results in an aver-
age hop distance of 150 m for 1000 vehicles. By contrast, it is
240, 260 and 330 m for Kakkasageri et al[47], CVoEG [28],
and the method proposed by Arkian et al. [21], respectively.
Figure 14 shows the hop distance versus vehicle density
curves on the right-hand y-axis and PD versus vehicle density
on the left-hand y-axis. the maximum delay is witnessed in
the method proposed by Arkian et al. [21] because it has a
maximum hop distance. The CH location in the method pro-
posed by Arkian et al. [21] is random, and it does not guaran-
tee the centrality of CH while the CH location in CVoEG [28]
is chosen based on the graph centrality. Nonetheless, the work
presented by Kakkasageri et al. [47] guarantees less delay
than the proposed work in [21] and [28] because the selection
of Ch is based on the neighbouring degree; this provides the
minimum hop distance. PD is low for a small average hop
distance. With the increase in vehicle densities, the average
hop distance increases and so is the PD. This finding validates
that HGCM clustering shows better performance for a sparse
network, which aligns with the general convention that a
crowded area increases PD. In sum, our HGCM reduces the
PD by approximately 25%, 41% and 48% compared with
the methods of Kakkasageri et al. [47], CVoEG [28] and
Arkian et al. [21], respectively, at high traffic.
Throughput depends on the number of packets received in
a small span. The minimum PD increases the throughput for
the proposed HGCM scheme irrespective of the number of
vehicles. Figure 15 shows the throughput curves. The hyper-
graph network presentation and novel set of CH selection
help achieve 460 kb/s throughput compared with 350, 330,
and 310 kb/s in other works at a density of 1000 vehicles.
The proposed scheme helps achieve consistently improved
throughput performance by approximately 31%, 39% and
48% compared with the methods of Kakkasageri et al. [47],
CVoEG [28] and Arkian et al. [21], respectively, for high
traffic.
VI. CONCLUSION AND FUTURE WORK
We have developed a novel cluster generation and mainte-
nance strategy in this study. The CH is chosen based on a
combination of four indicators that help maintain the stability
of the dynamic network. A changing structure and the fre-
quent connection and disconnection of communication links
amongst vehicles are modelled in a directed evolving hyper-
graph formulation of VANET. Spectral clustering creates the
ideal number of groups on the basis of the density of vehicles.
Each cluster has a single RSU at its centre. Relative velocity
score, eccentricity, neighbourhood degree and trust score are
all recommended in this study for finding the most stable CH
in each cluster. The proposed HGCM is tested for various
vehicle densities in a real area in Iraq’s capital, Baghdad.
Compared with individual measures and other techniques,
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our cumulative approach significantly improves CH stabil-
ity. The addition of the trust element results in 20% gain
in average CH stability over the combined performance of
three existing measures (i.e. relative speed, eccentricity and
neighbourhood). A one-hop network configuration is used to
evaluate the approach for different integrated network met-
rics, including packet latency and throughput. The average
packet distance travelled by the proposed method is 150 m
with a delay of 0.2 s, whereas the other comparative algo-
rithms under the same network conditions report a PD of
0.4 s for approximately 330 m according to the PD analysis
for the worst-case scenario (i.e. 1000 vehicles). Therefore,
HGCM has the lowest PD whilst still allowing for the shortest
possible hop distance. In addition, PD directly influences
throughput; hence, HGCM has the maximum throughput
compared with other methods.
In future work, we will attempt to generate more efficient
clustering by using a modularity matrix instead of an adja-
cency matrix. In addition, we intend to explore more metrics
for analysis, through which the proposed methodology can
be understood. The analysis of the algorithm’s computational
complexity will also be a benchmark of study in the next
part of this work. CH stability decreases with the increase in
vehicle density in the network. The solution can be verified
by increasing the number of clusters in the network in the
next part.
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MAYS KAREEM JABBAR was born in Amarah,
Misan, Iraq. She received the B.Sc. degree in com-
puter engineering from the Computer Engineering
and Information Technology Department, Univer-
sity of Technology, Baghdad, Iraq, in 2007, and
the master’s degree in wireless communications
networks from the Computer Engineering Depart-
ment, Eastern Mediterranean University (EMU),
Famagusta, Northern Cyprus, in 2014. She is cur-
rently pursuing the Ph.D. degree with the Com-
puter System Engineering Department, École Nationale d’Ingénieurs de Sfax
(ENIS), University of Sfax, Tunisia.
She is working as a Lecturer with the College of Engineering, University
of Misan, Misan. She is a member of the Smart Electric Vehicle Group at
the Computer Embedded System Laboratory, ENIS. Her current research
interests include VANET, V2V, and clustering algorithms.
HAFEDH TRABELSI studied at the École
Nationale d’Ingénieurs de Sfax (ENIS), from 1983
to 1989. He received the M.S. degree from the
École Centrale de Lyon, France, in 1990, the Ph.D.
degree from the University of Paris—XI, Orsay,
France, in 1994, and the Research Management
Ability degree from ENIS, all in electrical engi-
neering, in 2008.
He joined Tunisian University, in 1995. He is
currently a Professor of electric power engineering
with ENIS. Since 2013, he has been a Full Professor with the University
of Sfax, Tunisia, holding the Chair for Smart Electric Vehicle Group at
the Computer Embedded System Laboratory, ENIS. His research interests
include the design of new electric machines by using finite element method
and the implementation of advanced control systems for electric vehicle. His
on-going research is focusing on smart city and secure systems.
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