1. On Energy-Efficient Trap Coverage in Wireless Sensor Networks Junkun Li, Jiming Chen, Shibo He, Tian He, Yu Gu, Youxian Sun Zhejiang University, China University of Minnesota, US Singapore University of Technology and Design, Singapore Presenter: Qixin Wang The Hong Kong Polytechnic University, Hong Kong, China

2. No.2 Outline Introduction Problem formulation Algorithm design & analysis Numerical results Conclusion

3. No.3 Outline Introduction Background Related work Motivations

4. No.4 Background Allow existence of coverage holes Allow existence of coverage holes Require less sensor nodes Require less sensor nodes Guarantee the sensing quality of network Guarantee the sensing quality of network

5. No.5 Background Coverage hole The diameter of coverage hole is the maximum distance between any two points in the coverage hole.

6. No.6 Background Trap coverage proposed in [1] restricts the diameter of coverage hole. [1] P. Balister, Z. Zheng, S. Kumar, and P. Sinha. Trap coverage: Allowing coverage holes of bounded diameter in wireless sensor networks. In IEEE INFOCOM, 2009. Large diameter of coverage hole with limited area

7. No.7 Motivations  As sensor nodes could be deployed in a arbitrary manner, the required number of sensor nodes to ensure trap coverage is usually more than the optimal value.  How to provide trap coverage with minimum amount of active sensors ?  How to schedule the activation of sensors to maximize the lifetime of network ? Trap coverage Sleep wake-up strategy

8. No.8 Related Work  In [1], Balister et al consider the fundamental problem of how to design reliable and explicit deployment density required to achieve trap coverage requirement. Poisson distribution deployment is assumed in the paper.  In [2], an algorithm based on square tiling is proposed to schedule sensors with coverage hole existing. But it implicitly assumes the uniformity of sensor deployment, which may not be applicable in a randomly deployed WSN. [1] P. Balister, Z. Zheng, S. Kumar, and P. Sinha. Trap coverage: Allowing coverage holes of bounded diameter in wireless sensor networks. In IEEE INFOCOM, 2009. [2] S. Sankararaman, A. Efrat, S. Ramasubramanian, and J. Taheri. Scheduling sensors for guaranteed sparse coverage. http://arxiv.org, 2009.

9. No.9 Outline Problem formulation Network model Trap coverage Minimum weight trap cover problem Introduction

10. No.10 Network model  Disc sensing model with sensing range r  Transmission range is twice of sensing range  Sensors randomly deployed in a Region of Interest (RoI) and each sensor has an initial energy of E units which consumes one unit per slot if it is active

11. No.11 Trap coverage model  Coverage hole  D-trap coverage  Obviously, if we set diameter threshold D to zero, D-trap coverage reverts back to full coverage.

12. No.12  Weight/Cost assignment  Sensor with less residual energy is assigned with high weight/cost if activated.  Energy consumption ratio γ i  θ is a constant greater than 1.  If γ i =1, w is specially marked as infinity.  Problem Statement  The minimum weight trap cover problem is to choose a minimum weight set C* which can ensure that every coverage hole in A has a diameter no more than D, where D is a threshold set by applications. Minimum weight trap cover problem

13. No.13 10 Minimum Weight Trap Cover Problem 0 0 10 lifetime: 10 10 5 5 lifetime: 15 5 0 5 0 0 0 Example of energy balance

14. No.14 Outline Algorithm design & analysis Preliminaries Design Analysis Introduction Problem formulation

15. No.15 Preliminaries  Minimum weight trap cover problem is NP-hard  Intersection point  An intersection point is one of the two points where two sensors’ sensing boundaries intersect with each other.  Intersection point theorem  The diameter of a coverage hole equals to the maximum distance among all intersection points on the boundary of the hole.

16. No.16 How to achieve D-trap coverage A straight approach : Removal

17. No.17 Algorithm design -- I  Trap cover optimization (TCO) -- Overview  Basic idea: Derive a minimum weight trap cover C from a minimum weight sensor cover C’ which provides full coverage.  Main procedures:  Firstly, select a minimum weight sensor cover C’ which provides full coverage to the region.  Secondly, remove sensors iteratively from C’ until the required trap coverage can not be guaranteed.  Key challenge:  How to design optimum removal strategy? (Remove as much as possible)

18. No.18 Algorithm design -- II Case 1 Case 2 D ψ (i) = d D ψ (i) =d 1 +d 2 d1d1 d2d2 We introduce a variable, D ψ (i), to denote the diameter of coverage hole after removing sensor i from set ψ. Case 3 D ψ (i) =0 d

19. No.19 Algorithm design -- III Physical meaning of Σ i D ψ (i) : Up bound of coverage hole diameter if all these sensors are removed. Physical meaning of D ψ (i) : Up bound increment of coverage hole diameter if only sensor i is removed d 1 = D ψ (1) d q <d 1,d 2 <d q +D ψ (2) so, d 2 -d 1 < D ψ (2) dqdq d1d1 d2d2 D ψ (2)

20. No.20 Algorithm design -- IV  About D ψ (i)  We let D ψ (i) represent the largest possible increment of a coverage hole when removing sensor i from set ψ. D ψ (i) equals the sum of diameters of all coverage holes created by (only) removing sensor i from set ψ  The maximum increment of a coverage hole should be less than the diameter of sensing region 2r.  d· is the diameter of newly emerging coverage hole and M i is the number of newly emerging coverage holes.

21. No.21 Algorithm design -- V How to remove as much aggregate weight as possible ? 1. Remove sensor with high weight : w(i) 2. Remove more sensors.  Remove sensor with low D ψ (i) which restricts the largest increment of diameter. In this way, we can remove more sensors!  D ψ (i)=0 suggests it will not increase the diameter to remove i. 3 sensors D D 6 sensors

22. No.22 Algorithm design -- VI  We consider to normalize the weights of sensors by D ψ (i) to determine which sensor is to be removed. D ψ (i) is a variable between 0 and 2r. where D ψ (i) is a variable between 0 and 2r and α = 1/(2r).  We always remove sensor i with the largest G(i).  To guarantee the requirement of trap coverage, TCO only removes sensors which will not violate the D constraint. Key guidance :

23. No.23 Algorithm design -- VII TCO flow diagram

24. No.24 Algorithm design -- VIII 1 2 3 4 2 3 4 2 44 Step 1: C=Ø, C’={2,3,4} ψ = {2,3,4} Step 2: C=Ø, C’={2,4} ψ = {2,4} Step 3: C={2}, C’={4} ψ = {2,4} Step 4: C={2,4}, C’=Ø ψ = {2,4} 2

25. No.25 Algorithm analysis Let N C’ denote the number of sensors in C’. 1. The relationship between the weight of set C and C’ : 2. The relationship between the weight of set C and optimal solution: where Theoretical analysis:

26. No.26 Outline Numerical results Experiment setup Simulations Introduction Problem formulation Algorithm design & analysis

27. No.27 Experiment setup  The WSN in our simulations has N sensors, each with an initial energy of E units  Sensing range : 1.5 m  Square size : 10 m * 10 m  Algorithm overview  Naïve-Trap : A natural approach derived from Greedy-MSC [3] to meet the requirement of trap coverage.  Trap cover optimization (TCO) [3] M. Cardei, T. Thai, Y. Li, and W. Wu. Energy-efficient target coverage in wireless sensor networks. In IEEE INFOCOM, 2005.

28. No.28 Simulations -- I Active amount of sensors vs. time slot Average residual energy ratio of activated sensors vs. time slot

29. No.29 Simulations -- II Lifetimes

30. No.30 Outline Introduction Problem formulation Algorithm design & analysis Numerical results Conclusion

31. No.31 Conclusion The practical issue of scheduling sensors to achieve trap coverage is investigated in this paper. Minimum Weight Trap Cover Problem is formulated to schedule the activation of sensors in WSNs under the model of trap coverage. We propose our bounded approximation algorithm TCO which has better performance than the state-of-the-art solution. Future work Global- vs. Local- Disc sensing model vs. Probabilistic sensing model

32. No.32  Thank you!  Questions?