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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. Overview. Introduction Deployment problems of WSN

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modeling the communication problem in wireless sensor networks as a vertex cover

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

overview
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
introduction
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.
deployment problems of wsn
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.
the coverage problem
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.
the communication problem
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.
assumptions on wsn in solving the communication problem
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
the coverage sensors
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.
the communication sensors
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.
mathematical formulation of the communication problem
Mathematical formulation of the Communication problem

W

M

2

3

1

1

Cell

H

2

3

Demand

N

A service area to be monitored by WSN

mathematical formulation of the communication problem18
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.
mathematical formulation of the communication problem contd
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>

mathematical formulation of the communication problem contd20
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).
mathematical formulation of the communication problem contd21
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.
mathematical formulation of the communication problem contd22
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.

mathematical formulation of the communication problem contd23
Mathematical formulation of the communication problem(contd.)

S

CR

S10

S20

S4

Si

RC

S1

S5

S8

constraints of the mathematical formulation of the problem
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.
constraints of the mathematical formulation of the problem contd
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.
mathematical formulation of the communication problem contd26
Mathematical formulation of the communication problem(contd.)

Our objective function is to achieve a minimal vertex cover as stated

= 1 means a sensor device k has been allocated to be used as a vertex cover.

algorithm
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

algorithm contd
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.
algorithm contd29
Algorithm(contd)
  • In the evolution process relatively fit chromosomes reproduce new chromosomes and inferior chromosomes die until a desirable fitness is found.
genetic operations
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.
chromosome representation
Chromosome representation

chromosome

NULL

Vertex

Cover

NULL

NULL

NULL

Sensor Device

NULL

NULL

NULL

future direction
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.