1
MODELING THE COMMUNICATION PROBLEM IN
WIRELESS SENSOR NETWORKS AS A VERTEX COVER
by
Maytham Safar
Mohammad Taha
and Sami Habib
Presented by
Omar Haider Chowdhury
2
Overview
Introduction
Deployment problems of WSN
Assumption on WSN on solving the
communication problem
Mathematical formulation for
Communication problem
Algorithm for solving Communication
problem
Future work
References
3
Wireless sensor network (WSN)
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Introduction
Advancement in low power micro

electronic circuits, wireless
communications and operating system
have made Wireless Sensor network into
a feasible platform.
Initially WSN were dominated and
funded by the military applications i.e.
monitoring activity in battle field.
Now it is being used in many civilian
applications i.e. habitat and
environmental monitoring.
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Deployment problems of WSN
There are two core problems that
should be considered by
deployment of any wireless sensor
networks.
The Coverage problem.
The Communication problem.
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The Coverage problem
The Coverage problem is to place
sensor devices in a service area so that
the entire service area is covered.
The authors have proposed a heuristic
model to that maps the coverage
problem into two sub

problems:
floorplan and placement.
A combined optimization of both the
sub

problems results a good coverage
solution.
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The Coverage problem(contd.)
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The Coverage problem(contd.)
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The Coverage problem(contd.)
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The Coverage problem(contd.)
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The Coverage problem(contd.)
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The Communication problem
The communication problem is to
select a minimal set of placed
sensor devices in a service area
so that the entire area is
accessible by the minimal set of
sensors.
Finding the minimal set of sensors
is modeled as a vertex cover
problem.
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Assumptions on WSN in solving
the communication problem
In this work it is assumed that the
sensor networks consists of two
types of sensor devices.
The coverage sensors
The communication sensors
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The coverage sensors
It senses/monitors the
surrounding environments.
Generates data packet
periodically
Forwards the data from other
sensors towards the second types
of sensors.
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The communication sensors
It collects all the data generated
by the coverage sensors.
This kind of sensors have
sufficient processing capability
and power supply that make their
communication ranges cover the
whole service area.
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The communication
sensors(contd.)
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Mathematical formulation of
the Communication problem
1
2
3
…
M
1
2
3
…
N
Demand
Cell
W
H
A service area to be monitored by WSN
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Mathematical formulation of
the Communication problem
The service area, A,
with two
dimensional width(W) and
height(H) which is obstacle free.
The service area, A, is divided
into N * M cells, where each cell
can possibly contain a sensor
device at its centre of mass.
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Mathematical formulation of
the communication
problem(contd.)
A set of placed sensors for the
coverage problem, B, and TC are
given as the input of the
communication problem.
Each element in the set B is a
tuple, b(i), consisting of six
ordered parameters,
b(i) = <S(j), C(N*M), RC, SC,CR, BL>
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Mathematical formulation of
the communication
problem(contd.)
S(j) = The sensor identification number
C(N*M) = The physical cell location of the placed
sensor within the service area
RC = The radius of coverage of sensor S(j) in
meters
SC = Initial installation and deployment cost in
dollars ($)
CR = Communication radius, the radio signal
within S(j) can reach in meters.
BL = Battery level of S(j).
TC = The ratio of the total non

overlapping
radius of coverage of all placed sensors over the
total service area (W*H).
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Mathematical formulation of
the communication
problem(contd.)
Thus the communication
problem involves determining a
minimal subset of B, C, such that
the CR’s of all selected sensors
within B can reach all other
sensors in C’ = B
–
C.
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Mathematical formulation of
the communication
problem(contd.)
There are three possible
relations between CR and RC.
CR = RC
CR < RC
CR > RC
In this paper only the relation
CR > RC is considered as the
previous two relations has no
practical usage.
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Mathematical formulation of
the communication
problem(contd.)
S
RC
CR
S
i
S
10
S
4
S
1
S
8
S
5
S
20
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Constraints of the
mathematical formulation of
the problem
1 <= C <= B / z
A sensor which is not selected as
communication sensor must be in the
vertex cover of some communication
sensor.
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Constraints of the
mathematical formulation of
the problem(contd.)
L <= b(i) <= U
b(i) = the number of coverage sensor
in vertex cover of communication
sensor i
The number of overlapping sensors
should be minimized.
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Mathematical formulation of
the communication
problem(contd.)
Our objective function is to
achieve a minimal vertex cover
as stated
B
k
min
= 1 means a sensor device k
has been allocated to be used as
a vertex cover.
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Algorithm
begin
t =0;
initialize chromosomes P (t);
evaluate chromosomes P (t);
while (termination conditions are unsatisfied)
begin
t = t + 1;
select P (t) from P (t

1);
mutate some of P (t);
crossover some of P (t);
evaluate chromosomes P (t);
end
end
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Algorithm(contd)
A genetic algorithm is used to solve this
problem.
The initial population of the problem is the
chromosomes generated by applying the coverage
algorithm.
In each generation multiple chromosomes are
stochastically selected from the current
population and modified using operations
mutation and crossover to form the population
for the next generation.
A fitness function measures the quality of the
chromosomes based on the number of
communication sensors, number of chromosomes
covered by their sensing and communication
ranges.
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Algorithm(contd)
In the evolution process
relatively fit chromosomes
reproduce new chromosomes and
inferior chromosomes die until a
desirable fitness is found.
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Genetic operations
Mutation process : This operation
replaces an existed
communication sensor device with
a new one from the list of
coverage sensors.
Crossover process : This
operation combines features of
two selected chromosomes to form
two similar chromosomes.
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Chromosome representation
chromosome
NULL
NULL
NULL
NULL
NULL
NULL
NULL
Vertex
Cover
Sensor
Device
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Future Direction
The methodology used to solve this
problem can be improved.
Both the coverage problem and the
communication problem may be solved
simultaneously.
It is possible to solve both the
problems in such way that energy
utilization is reduced and overall cost
of setting up a WSN is reduced.
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Thank you
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