On Energy-Efficient Trap Coverage in Wireless Sensor Networks

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. Outline Introduction Problem formulation Algorithm design & analysis Numerical results Conclusion

3. Outline Introduction Background Related work Motivations

4. Background • Allow existence of coverage holes • Require less sensor nodes • Guarantee the sensing quality of network

5. Background Coverage hole The diameter of coverage hole is the maximum distance between any two points in the coverage hole.

6. Background Trap coverage proposed in [1] restricts the diameter of coverage hole. Large diameter of coverage hole with limited area [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.

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. 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. Outline Introduction Problem formulation Network model Trap coverage Minimum weight trap cover problem

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. 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. Minimum weight trap cover problem • Weight/Cost assignment • Sensor with less residual energy is assigned with high weight/cost if activated. • Energy consumption ratio γi • θ is a constant greater than 1. • If γi =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. Energy balance

13. Example of energy balance 10 0 10 0 10 10 lifetime: 10 10 5 5 10 5 10 10 0 5 0 lifetime: 15 0 0 • Minimum Weight Trap Cover Problem

14. Outline Introduction Problem formulation Algorithm design & analysis Preliminaries Design Analysis

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. How to achieve D-trap coverage • A straight approach : Removal

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. Algorithm design -- II Dψ(i) = d d1 d Dψ(i) =d1+d2 d2 Case 1 Dψ(i) =0 Case 2 Case 3 We introduce a variable , Dψ(i) , to denote the diameter of coverage hole after removing sensor i from set ψ.

19. Algorithm design -- III Physical meaning of Dψ(i) : Up bound increment of coverage hole diameter if only sensor i is removed Physical meaning of ΣiDψ(i) : Up bound of coverage hole diameter if all these sensors are removed. d1= Dψ(1) dq<d1,d2<dq+Dψ(2) so, d2-d1< Dψ(2) d2 d1 Dψ(2) dq

20. Algorithm design -- IV • About Dψ(i) • We let Dψ(i) represent the largest possible increment of a coverage hole when removing sensor i from setψ. Dψ(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 Mi is the number of newly emerging coverage holes.

21. Algorithm design -- V D D 3 sensors 6 sensors 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 Dψ(i) which restricts the largest increment of diameter. In this way, we can remove more sensors! • Dψ(i)=0 suggests it will not increase the diameter to remove i.

22. Algorithm design -- VI • We consider to normalize the weights of sensors by Dψ(i) to determine which sensor is to be removed. Dψ(i) is a variable between 0 and 2r. where Dψ(i) is a variable between 0 and 2r andα = 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. Algorithm design -- VII TCO flow diagram

24. Algorithm design -- VIII 2 2 3 3 Step 2: C=Ø, C’={2,4} ψ = {2,4} Step 1: C=Ø, C’={2,3,4} ψ = {2,3,4} 4 4 1 2 2 Step 3: C={2}, C’={4} ψ = {2,4} Step 4: C={2,4}, C’=Ø ψ = {2,4} 4 4

25. Algorithm analysis Theoretical analysis: Let NC’ 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

26. Outline Introduction Problem formulation Algorithm design & analysis Numerical results Experiment setup Simulations

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. Simulations -- I Active amount of sensors vs. time slot Average residual energy ratio of activated sensors vs. time slot

29. Simulations -- II Lifetimes

30. Outline Introduction Problem formulation Algorithm design & analysis Numerical results Conclusion

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. Thank you! • Questions?