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A New WSN Deployment Algorithm for Water
Pollution Monitoring in Amazon Rainforest Rivers
Zakia Khalfallah, Ilhem Fajjari†, Nadjib Aitsaadi‡, Rami Langar and Guy Pujolle
LIP6 – University of Paris 6 – 4, Place Jussieu, 75005 - Paris, France
†VIRTUOR: 4 Residence de Galande, 92320 Chatillon, France
‡LiSSi - University of Paris EST Creteil (UPEC): 122, rue Paul Armangot, 94400 Vitry Sur Seine, France
zakia.khalfallah@lip6.fr, ilhem.fajjari@virtuor.fr, nadjib.aitsaadi@u-pec.fr, rami.langar@lip6.fr, guy.pujolle@lip6.fr
Abstract—In this paper, we study the wireless sensor network
deployment for water pollution monitoring in the Amazon
rainforest rivers. Our objective consists in minimising the number
of deployed geographical field installations along the river, while
ensuring the detection of the substance spilled in the given river
regardless of the position of its source. A geographical field
installation is formed by a set of barrier coverage underwater
sensors which detect the pollutant if its molarity in the water is
greater than a predefined threshold. Indeed, the substance molar-
ity is inversely proportional to the moving distance. To generate
the best topology, we propose a novel geographic Installation
Field Deployment Algorithm based on the Backtracking heuristic
named BT-FIDA. Since the river has a several forks, in order to
reduce the number of installation fields, BT-FIDA minimises the
rate of at least 2-covered river segments. The simulation results
obtained show that our proposal minimises the number of field
installations (i.e., deployment cost) while minimising the rate of
areas which are miss-covered and over-covered.
Keywords: River monitoring, coverage, under-water WSN,
optimisation, backtracking heuristic.
I. INTRODUCTION
Over 97% of all the water on earth is salty and most of the
remaining 3% is frozen in the polar ice-caps [1]. The fresh
water contained in rivers, lakes and underground represent less
than 1%. Fresh water which is paramount necessity for human
life is a precious resource and the increasing pollution of our
rivers is a cause for alarm. Chemical waste products from in-
dustrial processes are willingly and/or accidentally discharged
into rivers, which is catastrophic for the biodiversity of fauna
and flora. We notice that in most of the industrial pollution
river disasters, the spilled substances include cyanide, zinc,
lead, copper, cadmium, mercury, etc. These substances may
seep into the water in such high concentrations so that fish and
other animals are immediately killed. Sometimes the pollutants
impact food chains and accumulate until they reach toxic
levels, eventually killing birds, fish and mammals.
In this paper, we tackle the underwater wireless sensor
network deployment problem for water monitoring in rivers. In
fact, this work is undertaken within the FP7 European project
“GOLDFISH” [2], which is focused on the monitoring of
water quality in the Amazon rainforest rivers. The objective
is to reduce the deployment cost by minimising the number
of geographical Field Installations (FI) along the river, while
guaranteeing the detection of a pollutant chemical substance
whatever the geographic area in which it is spilled (i.e.,
the pollution source). It is worth pointing out that each
geographical FI ensures a barrier coverage of a river and
any moving pollutant substance crossing a barrier is detected
if its molarity is greater than a predefined threshold. Indeed,
based on the propagation of a pollutant within water [3], the
substance concentration in water is inversely proportional to
its moving distance due to the river current. Based on the
latter water propagation model, two succeeding FIs cannot
be geographically separated by more than a predetermined
distance calculated with respect to the river’s proprieties and
the sensitivity of underwater sensors.
In order to generate the best FIs topology, we propose
a novel heuristic named Deployment Algorithm based on
Backtracking heuristic called BT-FIDA. Our proposal adopts
a “divide and conquer” strategy and operates as follows. First,
the river is modelised as a directed graph with many sources
(located in mountains) and one sink (located in the sea or
ocean). Then, BT-FIDA generates the prominent candidate
positions which could host FIs by applying three basic
heuristics: i) Max-FIDA, ii) Min-FIDA and iii) Avg-FIDA.
Afterwards, BT-FIDA runs a backtracking algorithm to select
the best candidate positions to deploy the FIs. Note that the
above three basic heuristics (i.e., Max-FIDA,Min-FIDA and
Avg-FIDA) make use of a recursive cut of the directed river
graph to generate the candidate positions. Based on exten-
sive simulations with a real river in the Amazon rainforest,
BT-FIDA obtains a good level of performance in terms of i)
number of FIs, ii) the rate of miss-covered segments and iii)
the rate of K-covered segments with K≥2.
The rest of this paper is organised as follows. The next
section will describe the architecture of the water river mon-
itoring system. In Section III, we will formulate the water
monitoring optimisation problem. Then, we will describe our
field installation deployment algorithm (BT-FIDA) and the
simulation results obtained, respectively in Section IV and
Section V. In Section VI, we will summarise the main research
papers related to the issue handled in this paper. Finally,
Section VII will conclude the paper.
II. ARCHITECTURE OF THE WATER RIVER MONITORING
SY ST EM
The water river monitoring system is composed of a set of
FIs deployed along the river and a set of gateways. In fact,
(a) FIs deployment (b) Components of an FI
Fig. 1. Architecture of water river monitoring system
each FI is associated with a single gateway deployed on a
bank of the river. Hereafter, we will describe the components
of i) the Field Installation and ii) the Gateway.
•The Field Installation: It is formed by a set of clusters
ensuring barrier coverage of a river. Indeed, we assume
that any chemical substance crossing the FI is detected.
In fact, the micro-deployment of clusters within the FI
is out of the scope of this paper and can be achieved
based on the related research work [4]. Each cluster is
composed of a set of static underwater sensors and one
surface water antenna. Indeed, the set of clusters within
each FI builds a static ad hoc network, which sends the
monitored events to the gateway. Note that a reactive or
proactive routing protocol can be installed within a cluster
network.
•The Gateway: is a centralised node that collects all
the detected events with an FI. Moreover, it sends the
detected alarms to the control room via a cellular and/or
satellite communication.
Fig. 1 summarises the global architecture of the water river
monitoring system and the components of an FI.
III. FORMULATION OF FIS DE PL OYM EN T PROBLEM
In this section, we will formulate the geographical field
installation deployment problem along the river. To do so, first
we propose to model the river as a directed graph denoted
by ~
G=V~
G, E ~
G, where V~
Gand E~
Gare
respectively, the sets of i) river’s forks and sources and ii)
river’s segments connecting the sources and forks. It is worth
pointing out that the direction of each segment e∈E~
G
is the same as the river’s current. In this work, we assume
that each fork w∈V~
Gcontains multiple incoming edges,
denoted by {e−
w}. Besides, we assume that it has only one
outgoing segment denoted by e+
wand its next-hop node is
denoted by w+. In other words, many streams merge to form
one larger canal. On the other hand, we assume that the river
carries the water in only one sea or ocean area. Hence, the
graph ~
Ghas many sources (i.e., nodes without incoming edges)
and only one sink (i.e., nodes without outgoing edges). Each
segment e∈E~
Gis characterised by its distance and the
average velocity of the water, respectively denoted by D(e)
and V(e).
The molarity level of a pollutant can be predicted as a
function of time and space making it possible to model the
behaviour of the solutes over the river course. As proposed
in [5], we model the concentration (i.e., molarity) time and
space function of a pollutant chemical substance in the river
water as:
C(x, t) = M
2·A√π·DL·t·exp −(x−U·t)2
4·DL·t(III.1)
where i) xis the distance in the downstream direction ex-
pressed in meters (m), ii) tis the duration between the spill
and the monitoring at point xexpressed in seconds (s), iii) M
is the mass of the contaminant expressed in kilograms, iv) A
is the cross-sectional area of the river expressed in m2, v) DL
and Uare, respectively, longitudinal dispersion and advective
velocity expressed in m2/s and m/s.
We notice that the concentration decreases as the moving
distance and the duration from the spill of the chemical
substance increases. Hence, the risk consists in no detecting
the pollutant since the underwater sensors can send the alarm if
and only if the substance’s molarity is greater than a predefined
threshold. Note that the latter reflects the hardware sensitivity
of the underwater sensors. In this sense, we can define a full-
river-coverage notion as the ability of the deployed FIs to
detect in the river a substance spilled anywhere.
Our objective is thus to minimise the cost of deployment,
while guaranteeing the full-river-covergae of the monitoring
system. The above objective (i.e., cost) can be evaluated by
the number of FIs denoted by NF I . To minimise the cost,
it is equivalent to maximise the distance between successive
FIs. Formally:
maximise "min
FI j∈ˆ
FI \{FIi}{d(FIi,FIj)}#,∀FIi∈ˆ
FI
(III.2)
where ˆ
FI is the set of deployed field installations and
d(FIi,FIj)is the euclidean distance separating FIiand
FIj.
On the other hand, we must guarantee the full-river-
coverage. To do so, the maximum distance between two
successive FIs cannot exceed a predefined distance Dth
which depends on the sensitivity of the hardware underwater
sensor. Formally,
min
FI j∈ˆ
FI \{FIi}{d(FIi,FIj)}≤Dth,∀FIi∈ˆ
FI (III.3)
We will now outline our geographic river filed installation
deployment problem, as follows:
∀FIi∈ˆ
FI
maximise minFI j∈ˆ
FI \{FIi}{d(FIi,FIj)}
subject to:
∀FIi∈ˆ
FI minFI j∈ˆ
FI \{FIi}{d(FIi,FIj)}≤Dth
Our problem is a non-linear multi-objective combinatorial
optimisation problem, which is NP-hard. In the next section,
we will propose a novel geographic Installation Field Deploy-
ment Algorithm based on the Backtracking heuristic called
BT-FIDA.
IV. PROPOSAL: FIELD INSTALLATION DE PL OYM EN T
ALG OR IT HM BA SE D ON BACKTRACK IN G HE URISTIC
The FI deployment problem is highly complex and the
generation of the optimal solution within a polynomial time
for a large scale river deployment is not possible. Thus,
we propose here a novel algorithm named Backtracking
based Installation Field Deployment Algorithm,BT-FIDA.
We notice that our problem is a combinatorial optimisation
problem. Thus, the size of the solution space is finite but is
exponential. Our proposal BT-FIDA operates as follows. First,
in order to minimise the number of combinations, hence the
time complexity, BT-FIDA generates the prominent candidate
positions (i.e., PS) to deploy FIs. To achieve this, BT-FIDA
runs three basic heuristics denoted by i) Max-FIDA, ii)
Min-FIDA and iii) Avg-FIDA. Then, BT-FIDA takes into
account the union of the above positions and runs a beam
search backtracking algorithm [6] [7] by building a partial
solution tree and selects the best one. The best branches are
explored by going down and going back up in the partial
tree solution until BT-FIDA converges to the best leaf (i.e.
the global solution). It is worth noting that the optimality is
impacted by the width of the partial tree solution and the cost
function φevaluating the solution in terms of i) number of
FIs (i.e., NF I ), ii) rate of miss-covered (i.e., Mcov ) and
ii) rate of K-covered (i.e.,Ocov) segments in the river with
Algorithm 1: BT-FIDA
1PSM in ←Min-FIDA (~
G,Dth)
2PSM ax ←Max-FIDA (~
G,Dth)
3PSAv g ←Avg-FIDA (~
G,Dth)
4PS ← PSM in ∪ PSM ax ∪ PSAvg
5FI-backtracking (~
G,PS, φ)
K≥2. The pseudo-algorithm of our proposal is summarised
in Algorithm 1.
In the following, we will explain in depth i) Min-FIDA,
ii) Max-FIDA, iii) Avg-FIDA and iv) FI-backtracking
heuristics.
A. Min-FIDA heuristic
The main idea behind the Min-FIDA heuristic consists in
deploying FIs recursively and by associating a level for each
node w∈V~
G. In this aim, we note all the source nodes
(i.e., without incoming edges) by W0={wi
0}and their level
is initialised to 0. Next, the level of each fork node w∈V~
G
is denoted by Lwand is equal to:
Lw= max
v∈W−{Lv}+ 1,(IV.4)
where W−is the set predecessor nodes of win directed graph
~
G. We note the fork nodes with level 1as W1={wi
1}.
Min-FIDA operates as follows. First, for each source node
wi
0∈ W0,Min-FIDA deploys an FI every Dth along its
corresponding outgoing edge e+
wi
0
and the process will be
deceased just after overtaken its successor fork node wi
1. Note
that e+
wi
0
is the link connecting wi
0to its successor node
wi
0
+=wi
1∈ W1. The set of FIs deployed after the fork
node wi
1is denoted by Swi
1. The deployed FIis are added
in the set PSmin but without including Swi
1. Once all the
source nodes have been explored, Min-FIDA deals with the
fork nodes W1. In fact, two cases can arise for each fork node
wi
1∈ W1.
1) The maximum distance between the wi
1and FIk∈ Swi
1
is located within e+
wi
1
(i.e., outgoing edge). We denote
the furthest field installation in Swi
1from wi
1by FIf.
Formally, FIfsatisfies the following constraint:
d(wi
1,FIf) = max
FI k∈Swi
1{d(wi
1,FIk)},(IV.5)
where d(wi
1,FIk)is the euclidean distance between the
fork node wi
1and FIk. In this case, Min-FIDA deploys
a field installation at FIf. Formally,
PSmin ← PSmin ∪ {FIf}(IV.6)
Then, Min-FIDA shrinks e+
wi
1
(i.e., outgoing link) by
moving the fork node wi
1to FIf. Moreover, all the
edges {e−
wi
1}(i.e., incoming links) and their correspond-
ing sources are removed from the directed graph ~
G.
Fig. 2. Min-FIDA: Graph reducing process
2) The farthest FIk∈ Swi
1from the fork node wi
1is not
deployed within its outgoing link e+
wi
1
. In other words, it
is deployed deeper in the graph ~
G. As above, FIfis the
furthest field installation in Swi
1from wi
1. In this case,
Min-FIDA adds a i) meta source node mnwi
1and a
ii) meta edge emnwi
1
between the meta node mnwi
1and
wi
1
+node. Note that wi
1
+is the successor of wi
1in ~
G.
The distance of the meta edge D(emnwi
1
)is set to the
distance of d(wi
1, wi
1
+)plus the (Dth −d(wi
1,FIf)).
Then, all the fork node wi
1’s incoming links and their
corresponding sources are removed from the directed
graph ~
G.
The above cases are depicted in Fig. 2.
Once all the fork nodes (i.e., W1) have been processed,
the new graph, denoted by ~
G0, is generated. As presented
above, it is formed by the same nodes and links of ~
Gexcept:
i) the source nodes W0and their outgoing links have been
removed, ii) W1’s outgoing links have been shrunk and iii)
meta source nodes and links could be added. Min-FIDA
applies recursively the same process for ~
G0until V~
G0=∅.
It is straightforward to see that the nodes of level 1become
sources in the new graph (i.e., level 0). We notice that
with this strategy, we will certainly obtain miss-covered river
segments since we select the farthest field installation from the
fork nodes. The pseudo algorithm of Min-FIDA heuristic is
summarised in Algorithm 2.
B. Max-FIDA heuristic
The heuristic is similar to Min-FIDA except in the way it
computes the moving destination of fork nodes W1(i.e. nodes
with level 1). The fork node wi
1∈ W1is moved to FIn, which
respects the following constraint:
d(wi
1,FIn) = min
FI k∈Swi
1{d(wi
1,FIk)}(IV.7)
It is straightforward to see that FInis the nearest field
installation to fork node wj
1. Moreover, we notice that with
this strategy, we will certainly obtain over-covered (i.e., no
hole of detection) river segments since we select the nearest
field installation from the fork nodes.
C. Avg-FIDA heuristic
As in the Max-FIDA heuristic, the same difference consists
with the way to compute the moving destination of fork nodes
W1(i.e. nodes with level 1). The fork node wi
1is moved to
the point PAvg , which respects the following formula:
PAvg =PF Ik∈Swi
1d(wi
1,FIk)
|Swi
1|(IV.8)
It is worth pointing out that Avg-FIDA will certainly obtain
both over and miss covered river segments since we select the
mean position of FIs deployed beyond a fork node.
D. FI-backtracking heuristic
Once the potential candidate deployment positions have
been generated PS, which is equal to PSM in ∪ PSM ax ∪
PSAv g,BT-FIDA runs the backtracking algorithm by
judiciously exploring the arrangement of all the prominent
positions in PS. Due to its high complexity for exploring
all possible solutions, we make use of the beam search
backtracking decision heuristic. In fact, it consists in keeping
only a predefined number Klimit of the best partial solutions,
in terms of cost function φat each level of the solution tree.
This will reduce the memory requirement and the exploration
time. Formally, the cost function is defined as:
φ= 1 −1
NFI ·Ocov
α·exp hMcog
βi(IV.9)
where αand βserve to normalise the parameters.We recall
that i) NFI is the number of deployed FIs, Mcov and Ocov
are the rates of respectively miss-covered and over-covered
(i.e., K-covered with K≥2) segments in the river. Note that
miss-covered metric Mcov is more penalising than the over-
covered metric. Hence, we apply the exponential function to
Mcov.
V. PE RF OR MA NC E EVALUATI ON
In this section, we will evaluate the performance of our
proposal BT-FIDA. To do so, first we will detail the sim-
ulation environment. Then, we will recall the performance
metrics. Afterward, we will briefly describe the baseline
FI Deployment Algorithm, denoted by Base-FIDA, used
for comparaison. Finally, we will illustrate the main results
obtained and highlight the benefit of our proposal BT-FIDA.
A. Simulation Environment
As mentioned in Section I, our proposal is validated within
a real Amazon Rainforest river. The map of the river is
illustrated in Fig. 3. We formulate the above river as a directed
graph with parameters illustrated in Table I.
TABLE I
PARAMETERS OF THE DIRECT RIVER GRAPH ~
G
Parameter Value
|V~
G|121
|E~
G|120
Pe∈E(~
G)(D(e)) 323.838 Km
Avg(D(e)) 2.7K m
Fig. 3. Amazon rainforest river map
Based on the inputs of our partner CapSenze company [8] in
FP7 GOLDFISH project according to their tests and hardware
sensors, the maximum distance Dth, in which a substance can
move within the river, while remaining detectable, is set to
6Km. In fact, beyond Dth , the pollution will be not detected.
We set the parameters of the cost function αand βto 2.
B. Performance Metrics
We recall hereafter, the main performance metrics to eval-
uate our deployment strategies of FIs within a river.
•NFI is the number of deployed FIs within ~
G
•Mcov is the rate of miss-covered edges among the whole
graph (i.e., Pe∈E(~
G)D(e))
•Ocov is the rate of K-covered edges among the whole
graph (i.e., Pe∈E(~
G)D(e)). That means the rate of
segments covered at least by two FIs.
C. Base-FIDA: baseline appraoch
For comparison purposes, we present here a simple de-
ployment strategy named Base-FIDA. It recursively deploys
BT−FIDA Min−FIDA Max−FIDA Avg−FIDA Base−FIDA
0
5
10
15
20
25
Percentage (%)
Over−covered areas
Miss−Covered areas
Fig. 4. Comparison of miss and over covered areas in river
FIs each Dth starting from the sink node of the river (i.e.,
sea and/or ocean). The process will be stopped until all
the sources nodes are covered. In fact, the deployment is
performed following the reverse direction of the current river.
The position of the first FI will be deployed at the sink node.
It is worth pointing out that Base-FIDA will guarantee 0%
of over and miss detected of segments in the rivers. However,
once Base-FIDA arrives to the source nodes, many FIs
will be deployed but cover a short segments compared to the
coverage range of any FI (i.e., Dth ).
D. Evaluation Results
As mentioned earlier, our proposal BT-FIDA will exploit
the prominent positions generated by Min-FIDA,Max-FIDA
and Avg-FIDA. In fact, we can see that our proposal is a
hybrid approach, which selects at each level the best posi-
tions obtained by the latter three heuristics. In Table II, we
present the results obtained by our proposal compared with the
baseline approach (i.e., Base-FIDA) and the aforementioned
heuristics: Min-FIDA,Max-FIDA and Avg-FIDA.
TABLE II
COST PERFORMANCE
Strategy NFI
BT-FIDA 23
Base-FIDA 54
Min-FIDA 19
Max-FIDA 34
Avg-FIDA 25
As we can see, our proposal BT-FIDA outperforms all
the heuristics and achieves the desired goal of minimising
the deployment cost (i.e., NFI ), while guaranteeing the full-
river coverage. In other words, the rate of lack-covered areas
MFI = 0%.
Specifically, as illustrated in Table II, our proposal reduces
the cost of deployment by 32.35% compared to Max-FIDA,
while guaranteeing the full-coverage of the whole river as
depicted in Fig. 4. On the other hand, BT-FIDA needs only
more 4field installations than Min-FIDA in order to remove
the hole detection. We notice that the Avg-FIDA heuristic
presents both hole and over detected areas within a network,
which may miss the propagation of the pollutant. Besides, our
16.6
16.8
17
17.2
17.4
17.6
17.8
15 20 25 30 35 40 45
Rate of over-covered areas
Partial tree solutions width
Fig. 5. Impact of Klimit
proposal reduces the number of FIs compared to the average
heuristic.
As expected, the baseline approach shows the worst results.
In fact, since the deployment starts from the destination (i.e.,
sea and/or ocean), the strategy will deploy many FIs nearest
the sources, which cover tiny segments. This explains its
highest cost. However, Base-FIDA ensures 0% of over and
miss detected segments. We notice that our proposal reduces
the deployment cost by 57.40% compared to the baseline,
while the constrains are not violated.
In Fig. 5, we illustrate the impact of the size of the best
partial solution at each level of the solution tree. We notice
that even Klimit our proposal deploys the same number of
FIs, which is equal to 23 and guarantees a full-coverage.
On the other hand, we notice that the reduction of the rate
of over-covered segment is tiny. Consequently, we conclude
that setting Klimit to 15 is sufficient and the performance are
steady.
VI. RE LATE D WO RK
To the best of our knowledge, there is no research paper
tackling the geographical filed installation deployment prob-
lem in rivers. In fact, i) the stream river direction, ii) river
topology and iii) the propagation model of pollutant substances
in rivers makes the underwater sensor network deployment
problem atypical and more challenging. Indeed, the classical
coverage definition of an area is not valid and it has been
evolved in our paper. However, hereafter we will describe
the main network deployment research fields, which are very
close to our problematic but unfortunately the related strategies
cannot be used.
In [9] [10], the authors aimed to develop novel remote real-
time monitoring technologies that can continuously collect
water quality parameters in lakes, rivers and reservoirs. The
system can be used to investigate various water quality param-
eters for real time surveillance by remote users via Internet.
Unfortunately, the deployment problem of sensors has not been
addressed.
In literature, the classical deployment issue of terrestrial
sensor networks has been studied in depth. In fact, we can
classify them in three groups. First, the random strategies [11]
in which the sensors are randomly deployed with respect to
a predefined random distribution. The second is a regular
deployment [12] [13] algorithms, which make use of basic
structures such as: triangle, square, polygon, hexagon, etc.
Finally, virtual force approaches [14] in which sensors move
by attractive and/or repulsive forces of neighboring sensors
and obstacles until the convergence to the steady state (i.e.,
best topology). Unfortunately, the above proposals cannot be
applied. In fact, the coverage definition and the assumptions
(e.g. target propagation model, topology of deployment area,
etc.) are different than those of field installation deployment
problem in rivers.
The underwater 2-dimensional and 3-dimensional deploy-
ment algorithms [15] [16] proposed in literature cannot be
applied within a water monitoring of rivers context. Indeed,
all the sensor nodes are deployed at the same depth with
two-dimensional strategies and sensor nodes may be floating
at an arbitrary one with three-dimensional approaches. We
notice that the above methods focused on the event detection
within a predefined small zone and the monitored event moves
only in this latter. The proposed strategies do not deal with
different geographical zone (i.e., field installations), which
are correlated in term of sensing coverage range in a river.
Noting that the above methods can be exploited within one
field installation in the river to guarantee full barrier coverage
and reduce the needed number of sensors.
The second research filed similar to our problem is the
urban traffic surveillance based on wireless sensor net-
works [17] [18] [19]. In fact, we can say that a river is
comparable to road map and the river current to the traffic
flow. Nevertheless, the road traffic is bidirectional and the
pollutant target substance spreading has a unique sense. This
considerably affects the way of sensor placement. Moreover,
a car cannot disappear in the road. It means that even if roads
present a large hole of coverage areas, the system will be
able to detect the cars by focusing the deployment in the road
connection points. It is not the case for pollutant substance
monitoring in which the detection strongly depends on its
molarity.
VII. CONCLUSION
In this paper, we studied the underwater sensor network
deployment problem for river monitoring. To the best of
our knowledge, we are the the first to tackle this problem.
We proposed a novel deployment algorithm called BT-FIDA
based on the backtracking and beam search heuristics. The
proposal is validated with a real river in Amazon rainforest.
Through extensive simulation results, we have shown that
the deployment cost is minimised and the full-coverage is
guaranteed.
Acknowledgments This work is supported by the European
commission within the FP7 GOLDFISH Project. We would like
to thank all the partners of GOLDFISH project.
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Algorithm 2: Min-FIDA heuristic
1Inputs: ~
G=V~
G, E ~
G,Dth
2Output: PSM in
3PSM in ← ∅
4~
G0←~
G
5while V~
G06=∅do
6W0← {w∈V~
G0:Lw= 0}
7W1← {w∈V~
G0:Lw= 1}
8foreach wi
0∈ W0do
9wi
1←wi
0+(successor of wi
0)
10 Swi
1← ∅
11 P os ←position(wi
0)
12 k←0
13 while wi
1is not overtaked do
14 Deploy a FIkwhich is Dth away from P os
15 if FIkovertakes wi
1then
16 Swi
1← Swi
1∪ {FIk}
17 else
18 PSM in ← PSMin ∪ {F Ik}
19 P os ←position(FIk)
20 k←k+ 1
21 V~
G0←V~
G0\W0(remove source
nodes)
22 E~
G0←E~
G0\ ∪w∈W1{e−
w}(remove
incoming links)
23 foreach wj
1∈ W1do
24 Locate FIfsatisfying:
d(wi
1,FIf) = maxF I k∈Swi
1{d(wi
1,FIk)}
25 PSM in ← PSMin ∪ {F If}
26 if FIfis deployed within e+
wi
1
then
27 Position of wi
1is moved to FIf
28 else
29 V~
G0←V~
G0∪ {mnwi
1}(add
meta-node)
30 E~
G0←E~
G0∪ {emnwi
1}(add
meta-link between mnwi
1and wi
1
+)
31 D(emnwi
1
)←
d(wi
1, wi
1
+)+(Dth −d(wi
1,FIf))
32 V~
G0←V~
G0\{wi
1}
33 E~
G0←E~
G0\{ewi
1}
