EnergyEfficient Target Coverage in Wireless Sensor Networks

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Energy-Efficient Target Coverage in Wireless
Sensor Networks

• Mihaela Cardei, My T. Thai, Yingshu Li, Welli Wu
• INFOCOM 2005
• Presented by Jae-Hoon Jung

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Contents

• Introduction
• Target coverage problem
• Related work
• Maximum set covers problem
• Problem formulation
• Two heuristics
• LP-MSC heuristic
• Greedy-MSC heuristic
• Simulation results
• Conclusion

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Introduction (1/2)

• Power-constrained wireless sensor networks
• Prolonging network lifetime through power saving
  technique
• Sensor scheduling
• Active mode vs. sleep mode
• Coverage problem
• Given
• Field
• N sensor nodes
• Question
• How well can the field be monitored?
• Maximizing network lifetime by sensor scheduling

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Introduction (2/2)

• Area coverage problem
• Sensing overall area
• Minimizing active nodes
• Maximizing network lifetime
• Target coverage problem
• Sensing all targets
• Minimizing active nodes
• Maximizing network lifetime

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Related Work (1/2)

• 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

Disjoint set cover Same time interval
Non-disjoint set cover Different time interval
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Related Work (2/2)
C s1, s2, s3, s4 R r1, r2, r3 Sensors
lifetime 1
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
Disjoint sets S1 s1, s2 S2 s3,
s4 Lifetime G 2
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Maximum Set Covers (MSC) Problem

• 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
• Each sensor is not active more than 1
• MSC is NP-Complete

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Problem Formulation (1/3)

• Using Linear Programming Approach
• Given
• A set of n sensor nodes C s1, s2, , sn
• A set of m targets Rr1, r2, , rm
• The relationship between sensors and targets
• Ck isensor 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

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Problem Formulation (2/3)
maximize network lifetime
sensors lifetime constraint
all targets must be covered
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Problem Formulation (3/3)
0 yij tj 1
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LP-MSC Heuristic

• Initial G 0
• Let be the optimal solution of the LP
  formulated before
• First approximation can be obtained as follows
• Set
• For each k, choose an
• Update the network lifetime
• Update the remaining lifetime for each sensor

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LP-MSC Heuristic

• Iteratively repeat step 1 and 2 by solving this
• Return G if there is no longer any set that can
  cover all targets

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Greedy-MSC Heuristic

• Select critical target
• Target most sparsely covered
• Select sensor
• Covers critical target
• Covers a large number of uncovered targets

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Simulation environment

• Stationary sensor and target
• Randomly located in 500m 500m
• Number of sensor nodes
• 25 750
• Number of targets
• 5 15
• Sensing range
• 100m 300m
• Solving linear programming
• Using optimization toolbox in Matlab

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Simulation results

• Network lifetime with number of sensors with
  range r 250m

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Simulation results

• LP-MSC heuristic, network lifetime with number of
  sensors for 10 targets

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Simulation results

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

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Conclusion

• Contributions
• Proposing maximum set covers approach
• Proving its NP-completeness
• Proposing an efficient heuristic
• Using a LP formulation
• Using greedy approach
• Future work
• k-coverage
• p-coverage

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NP-completeness of MSC

• Theorem MSC is NP-Complete
• Proof
• First, define the Decision Version of MSC
  problem.
• To show that MSC ? NP
• Given a family of set covers S1, , Sp with time
  weights t1, , tp, and the number k.
• Then we can verify in polynomial time whether the
  set covers meet the requirements
• To prove the decision version of MSC is NP-hard
• Reduce 3-SAT problem to it in polynomial time

Given a collection C of subsets of a finite set
R, and a number k, find a family of set covers
S1,..., Sp with time weights t1,..., tp in 0, 1
such that t1 tp k and for each subset s
in C, s appears in S1, , Sp with a total weight
of at most 1, where 1 is the lifetime of each
sensor.
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LP-MSC Heuristic

• Runtime complexity

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Greedy-MSC Heuristic

• Select critical target
• Target most sparsely covered
• Select sensor
• Covers critical target
• Covers a large number of uncovered targets
• Runtime complexity
• O(dm2n)
• d the number of sensors that covers
  most sparsely covered target

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Simulation results

• Runtime of LP-MSC and Greedy-MSC heuristics