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This paper addresses the critical issue of power scarcity in wireless sensor networks by proposing a Maximum Set Covers (MSC) approach to optimize sensor energy utilization. The paper introduces the MSC problem, proves its NP-Complete nature, and presents two heuristics to tackle it. The paper outlines an Integer Programming model and a Greedy Heuristic to efficiently solve the MSC problem and maximize target coverage while minimizing energy consumption. By scheduling sensor node activities to alternate between sleep and active modes, the proposed approach offers a practical solution to enhance energy efficiency in wireless sensor networks.
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Energy-Efficient Target Coverage in Wireless Sensor Networks PLLAB 김성민
Outline • Introduction • Proposal • Maximum Set Covers(MSC) Problem • MSC Problem is NP-Complete • MSC heuristic • Conclusion
Introduction • Characteristics of WSN • Dense • Limited resourse • … Critical Issue: Power Scarcity!!!
Target Coverage Problem • Given • m targets • n sensors randomly deployed • Assume • same remaining energy • same range • How to optimize the sensor energy utilization?
Proposal C = {s1, s2, s3, s4} R = {r1, r2, r3} Disjoint sets: S1 = {s1, s2} S2 = {s3, s4} Lifetime G = 2 Our Approach: S1 = {s1, s2} with t1 = .5; S2 = {s2, s3} with t2 = .5 S3 = {s1, s3} with t3 = .5; S4 = {s4} with t4 = 1 Lifetime G = 2.5
Maximum Set Covers (MSC) • Given C : set of sensors R : set of targets • Goal • Determine a number of set covers S1, …, Sp and t1,…,tp • Where: • Si completely covers R • Maximize t1 + … + tp
Maximum Set Covers (MSC) • Theorem: MSC is NP-Complete • MSC problem belongs to the class NP and is NP-hard, so MSC is NP-Complete • Proof ???? • So, this paper presents Two heuristics.
MSC Heuristic • We first model the MSC problem as an Integer Programming • Given : • A set of n sensor nodes: 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} s1 r1 C = {s1, s2, s3}; s2 r2 R = {r1, r2, r3} s3 r3 C1 = {1,3}; C2 = {1,2}; C3 = {2,3} • Variables: • xij = 1 if si ∈ Sj, otherwise xij = 0 • tj ∈ [0, 1], represents the time allocated for Sj
MSC Heuristic (IP) • first constraint : each sensor life time <=1 • second constraint : each target is covered by at least one sensor
MSC Heuristic (IP) • The term xijtj is not linear • Therefore we set yij = xijtj
MSC Heuristic (LP) • We are ready to introduce LP-MSC heuristic
MSC Heuristic (LP) O (p3n3)
Greedy Heuristic • Input parameter • C - the set of sensors • R - the set of targets • w – sensor lifetime granularity, 0 < w <= 1
Greedy Heuristic O (im2n)
Conclusion • Schedule the sensor node activity to alternate between sleep and active mode • Our contributions: • Propose maximum covers set approach • Prove it is NP-complete • Propose an efficient heuristic