1. Energy-Efficient Target Coverage in Wireless Sensor Networks Mihaela Cardei, My T. Thai, YingshuLi, WeiliWu Annual Joint Conference of the IEEE Computer and Communications Societies, 2005. INFOCOM 2005

2. Outline  Itroduction  Related Work  Target Coverage Problem  Maximum Set Covers  Solutions To Compute Maximum Set Covers LP-MSC Heuristic Greedy-MSC Heuristic  Simulation  Conclusions

3. 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.

4. 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.

5. 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.

6. 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

7. 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 mechanism Step1 、 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

8. 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 S 1, …, S p with time weight t 1,…, t p in [0,1] Goal ： to maximize t 1 +…+ t p

9. Disjoint set ： S 1 = {s 1, s 2 } t 1 =1 S 2 = {s 3, s 4 } t 2 =1 Lifetime G = 2 R = {r 1, r 2, r 3 } C = {s 1, s 2, s 3, s 4 }

10. Maximum Set Covers ： S 1 = {s 1, s 2 } t 1 = 0.5 S 2 = {s 2, s 3 } t 2 = 0.5 S 3 = {s 1, s 3 } t 3 = 0.5 S 4 = {s 4 } t 4 = 1 Lifetime G = 2.5

11. 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 S 1, …, S p with time weight t 1,…, t p such that t 1 +…+t p ≧ k?  Then we can verify in polynomail time whether t 1 +…+t p ≧ k target is covered by at least one sensor Sensor appears in S 1 …S p with total weight is 1 MSC ∈ NP  Reduce the 3-SAT problem to MSC in polynomial time MSC ∈ NP-hard

12. 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 = {s 1, s 2, …, s n } a set of m targets: R={r 1, r 2, …, r m } The relationship between sensors and targets: C k = { i | sensor s i covers target r k } x ij ， boolean variable ， sensor s i in the set cover S j t j ， the time allocated for the set cover S j  The optimization problem can be written as ：

13.  set y ij = x ij t j ， and reformulate the problem ：

14. 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

15. 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(p 3 n 3 )

16. LP-MSC Example s 1 r 1 C = {s 1, s 2, s 3 }; R = {r 1, r 2, r 3 } s 2 r 2 C 1 = {1,3} C 2 = {1,2} C 3 = {2,3} s 3 r 3 S 1 = {s 2, s 3 } S 2 = {s 1, s 3 } S 3 = {s 1, s 2 } T 1 = 0.333 T 2 = 0.333 T 3 = 0.333 G = 1 S 1 = {s 2, s 3 } S 2 = {s 1, s 3 } S 3 = {s 1, s 2 } T 1 = 0.111 T 2 = 0.111 T 3 = 0.111 G = 1.333 G = 1.5

17. 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 C i : 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

18. Greedy-MSC Heuristic  Condition : each target is covered by at least one sensor  Step1 ： select a critical target r critical ∈ TARGETS  Step2 ： heuristic selects the sensor (s u ) with the greatest contribution that covers the critical target  Step3 ： C i = C i ∪ s u for all target r k covered by s u ， TARGETS = TARGETS - r k When all targets are covered ， the new set cover was found for all sensor s j ∈ C i ， lifetime_s j = lifetime_s j – w  Step4 ： Return the set covers C 1 ， C 2 ， … ， C i  runtime complexity ： O(im 2 n) i is upperbounded by d / w ， d is the number of sensors covers the most sparsely covered target.

19. 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

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

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

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

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

24. Runtime of LP-MSC and Greedy-MSC heuristics

25. 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.