Energy-Efficient Target Coverage in Wireless Sensor Networks

Mihaela Cardei, My T. Thai, YingshuLi, WeiliWuAnnual Joint Conference of the IEEE Computer and Communications Societies, 2005.

INFOCOM 2005

Outline Itroduction Related Work Target Coverage Problem Maximum Set Covers Solutions To Compute Maximum Set Covers

LP-MSC Heuristic Greedy-MSC Heuristic

Simulation Conclusions

Introduction Application of sensor networks ：

National security 、 Surveillance 、 Health care Environment monitoring

A critical issue in wireless sensor networks is power scarcity.

Methods that optimize the sensor energy utilization have great importance.

Introduction A sensor node’s radio can be one of following four states ：

transmit 、 receive 、 idle 、 sleep

A analysis of the power usage (presented in [14]) transmit 0.38w~0.7w receive 0.36w idle 0.34w sleep 0.03w

Selecting the state of each sensor node’s radio is accomplished through a scheduling mechanism.

[14] V. Raghunathan, C. Schurgers, S. Park, and M. B. Srivastava,Energy-Aware Wireless MicrosensorNetworks, IEEE Signal Processing Magazine, 19 (2002), pp 40-50.

Introduction Power saving techniques can generally be

classified in the following categories ： schedule the wireless nodes to alternate between active

and sleep mode power control by adjusting the transmission range of

wireless nodes energy efficient routing, data gathering reduce the amount of data transmitted and avoid useless

activity.

Related work Disjoint Set Covers

Divide sensor nodes into disjoint sets Each set completely monitor all targets One set is active each time until ran out of energy Goal: To find the maximum number of disjoint sets This is NP-Complete

Target Coverage Problem Definition ： Target Coverage Problem(TCP)

m targets with known location n sensors randomly deployed in the closed proximity of the targets schedule the sensor nodes activity all the targets are continuously observed and network lifetime is

maximized.

Scheduling mechanismStep1 、 Sensors send their location information to the BS

Step2 、 BS executes the sensor scheduling algorithm and broadcasts the schedule when each node is

active

Step3 、 Every sensor schedules itself for active/sleep intervals

Maximum Set Covers Definition ： MSC Problem

C: set of sensors （ n sensors ） every sensor can be part of more than one set assume each sensor’s lifetime is 1

R: set of targets （ m targets ） Find a family of set covers S1, …, Sp with time

weight t1,…, tp in [0,1]

Goal ： to maximize t1+…+ tp

Disjoint set ：

S1 = {s1, s2} t1=1

S2 = {s3, s4} t2=1 Lifetime G = 2

R = {r1, r2, r3}

C = {s1, s2, s3, s4}

Maximum Set Covers ：

S1 = {s1, s2} t1 = 0.5S2 = {s2, s3} t2 = 0.5S3 = {s1, s3} t3 = 0.5S4 = {s4} t4 = 1

Lifetime G = 2.5

MSC is NP-complete

First,define the decision version of the MSC problem Given a number k Does it exist a family of set covers S1, …, Sp with time

weight t1,…, tp such that t1+…+tp k?≧ Then we can verify in polynomail time whether

t1+…+tp k≧ target is covered by at least one sensor Sensor appears in S1…Sp with total weight is 1 MSC NP∈

Reduce the 3-SAT problem to MSC in polynomial time MSC NP-hard∈

Solutions To Compute Maximum Set Covers Integer programming formulation of the MSC problem

Set a bound p for the number of ser-covers a set of n sensors: C = {s1, s2, …, sn} a set of m targets: R={r1, r2, …, rm} The relationship between sensors and targets:

Ck = { i | sensor si covers target rk} xij ， boolean variable ， sensor si in the set cover Sj

tj ， the time allocated for the set cover Sj

The optimization problem can be written as ：

)Ssiff(x,xwhere

,..,p,jRrx

Cstxtosubject

t...tMaximize

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set yij = xijtj ， and reformulate the problem ：

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LP-MSC heuristic

Initial: G = 0 Step1 ： Let be the optimal solution

of the LP. Step2 ： First approximation can be obtained as follows:

for j = 1 to p ， set

for k = 1 to m ,choose an

after the first approximation each sensor has remaining life time network lifetime

*0 maxmin ijCikj ytk

,1,1),,( ** pjnity jij

0.,. 0000* ijjijjijk yotherSettysettystCi

p

jiji yT

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LP-MSC heuristic Step3 ： Iteratively repeat step 1 and 2 by solving the

following linear program

Step4 ： Return the network lifetime G runtime complexity ： O(p3n3)

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LP-MSC Example

s1 r1 C = {s1, s2, s3}; R = {r1, r2, r3}

s2 r2 C1 = {1,3} C2 = {1,2} C3 = {2,3}

s3 r3

667.0

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S1 = {s2, s3}

S2 = {s1, s3}

S3 = {s1, s2}

T1 = 0.333

T2 = 0.333

T3 = 0.333

G = 1

222.0

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S1 = {s2, s3}

S2 = {s1, s3}

S3 = {s1, s2}

T1 = 0.111

T2 = 0.111

T3 = 0.111

G = 1.333G = 1.5

Greedy-MSC Heuristic

The input parameters C: set of sensors R: set of targets w: sensor lifetime granularity ， w (0,1]∈ i : the number of set covers Ci: the set cover

Initial ： set each sensor lifetime to 1 Maintain two sets ：

SENSORS ： the list of sensors that have the residual energy greater than zero

TARGETS ： contains the targets that still have to be covered

Greedy-MSC Heuristic Condition : each target is covered by at least one sensor Step1 ： select a critical target rcritical TARGETS∈ Step2 ： heuristic selects the sensor (su) with the greatest

contribution that covers the critical target Step3 ：

Ci = Ci s∪ u for all target rk covered by su ， TARGETS = TARGETS - rk When all targets are covered ， the new set cover was found for all sensor sj C∈ i ， lifetime_sj = lifetime_sj – w

Step4 ： Return the set covers C1 ， C2 ，…， Ci runtime complexity ： O(im2n)

i is upperbounded by d / w ， d is the number of sensors covers the most sparsely covered target.

Simulation Results sensors and targets randomly located in a

500m * 500m area assume the sensing range is equal for all the

sensors in the network tunable parameters:

n , the number of sensor nodes: 25~75 m , the number of targets: 5~15 r, the sensing range:100~300 m

Take p = n

Network lifetime with number of sensors when range r=250m

LP-MSC heuristic, network lifetime with number of sensorsfor 10 targets

LP-MSC heuristic, lifetime and number of iterations for tolerance 0.1 (a.) and tolerance 0.01 (b.)

Greedy-MSC, network lifetime for 5 targets and range r=250m

Runtime of LP-MSC and Greedy-MSC heuristics

Conclusions Wireless sensor networks are battery powered ,

therefore prolonging the network lifetime is highly desirable.

An efficient method is to schedule the sensor node activity to alternate between active and sleep mode.

One solution is to organize the sensors in set covers which are activated in turn. This problem is modeled as maximum set covers problem.

Future work ：k-coverge and p%-coverage on the network lifetime.