1. Efficient Point Coverage in Wireless Sensor Networks Jie Wang and Ning Zhong Department of Computer Science University of Massachusetts Journal of Combinatorial Optimization, vol. 11, no. 3, May 2006 SCIE Impact Factor: 0.291

2. 2 Outline Introduction ILP model Approximation Algorithm Simulation Conclusion

3. 3 Introduction Coverage research directions 1. Design communication protocols 2. Investigate coverage measures 3. Achieve maximum network lifetime 4. Find a minimum-cost sensor placement

4. 4 Introduction – The Minimization Problem t 1, …, t l types of sensors with radius r 1, …, r l and costs C 1, …, C l r 1 < r 2 < … < r l There are n discrete points in the sensing field R  may or may not be grid points  a sensor can only be place on a point (also called a site)

5. 5 Introduction – The Minimization Problem To find a selection of sensors and a subset of sites to place these sensors such that  every point in R is covered by at least σ sensors  the total cost of the sensors is minimum

6. 6 ILP Model – Preliminary Euclidean distance between point i and point j i

7. 7 ILP Model Coefficients: = the cost of a type- t v sensor 0-1 Integer Variables:

8. 8 ILP Model Each point is covered by at least σ sensors Each point can only place at most one sensor

9. 9 Approximation Algorithm Solve the relaxed LP and get the optimal LP solution Convert the optimal LP solution to an integer solution for the ILP Relax the Integer Linear Programming to the Linear Programming Formulate the problem using the Integer Linear Programming

10. 10 Approximation Algorithm The main idea:  Construct a graph G=(V,E)  Start from point I with the largest degree  Select the σ largest values that can cover i  Remove point i and any other point form R that is also covered by these σ sensors

11. 11 Approximation Algorithm

12. 12 Approximation Algorithm

13. 13 Approximation Algorithm

14. 14 Approximation Algorithm

15. 15 Approximation Algorithm

16. 16 Simulation – Grid Sensing Fields LP solver: lpsolve 5.5 Sensing range: r A = 100m, r B = 200m Cost of sensors: C A = 75 or 100 USD C B = 200 USD

17. 17 Simulation – Grid Sensing Fields C A = 75 m C A = 100 m

18. 18 Simulation – Randomly Points LP solver: lpsolve 5.5 Sensing field: 10x10 Sensing range: r A = 0.5, r B = 1.0 Cost of sensors: C A = 100, C B = 200

19. 19 Simulation – Randomly Points

20. 20 Conclusion Present a polynomial-time approximation algorithm The approximation ratio γ may be large In practice, the actual approximation ratio is small

21. 21