1. Energy-Efficient Sensor Network Design Subject to Complete Coverage and Discrimination Constraints Frank Y. S. Lin, P. L. Chiu IM, NTU SECON 2005 Presenter: Steve Hu

2. Outline Problem Description Problem Formulation Solution Procedure Computational Results Conclusion

3. Problem Description The detection radius of sensor is 1 A complete coverage/discrimination sensor field with 3 by 5 grids

4. Problem Description Completely discriminated: unique power vector for each grid point Ex: for grid point (1,3) for grid point (3,2)

5. Problem Description If we want to prolonged life time K times, two options: –(1) Deploy K duplicate sensor networks on a sensor field –(2)No duplicate sensor networks, but divide the network in K covers

6. Overall placementCover 1 Cover 2Cover 3

7. Problem Description No duplicate but divide in 3 covers Total sensor number: 14 Duplicate 3 times Total sensor number: 6 * 3 = 18

8. Problem Description Lemma 1 –G r : the number of covering grids

9. Problem Description Lemma 2: A grid point can be covered by a set of sensors. The maximum cardinality of the set exactly equals the number of covering grid points of a sensor that is allocated in the grid point.

10. Problem Description Lemma 3: On rectangular sensor field with a finite area, the upper bound of the number of covers, U r, is

11. Problem Description By Lemma 3

12. Problem Formulation Given Parameters: A = {1,2,…,m}: The set of indexes for candidate locations where sensor can be allocated. B = {1,2,…,n}: The set of the indexes for grid points that can be covered and located by the sensor network, m <= n K: The number of covers required (with upper bound regards to radius) a ij : Indicator which is 1 if grid point i can be covered by sensor j, and 0 otherwise c j : Cost function of sensor j

13. Problem Formulation Decision Variables: X jk : 1 if sensor j is designated to cover k of sensor network, and 0 otherwise Y j : Sensor allocation decision variable, which is 1 if sensor j is allocated in the sensor network and 0 otherwise

14. Problem Formulation Objective function:

15. Problem Formulation Constraints: A: candidate sensor location B: every grid point in the field aij: 1 if grid point i can be covered by sensor j, and 0 otherwise (Coverage Constraint)

16. Problem Formulation Constraints: (Discrimination Constraint)

17. Solution Procedure Lagrangean Relaxation –a method for obtaining lower bounds (for minimization problems) –Ex:

18. Solution Procedure Lagrangean Relaxation ( ) with

19. Lagrangean Relaxation ( ) This (19.5) is the smallest upper bound we can found by Lagrangean Relaxation. Solution Procedure

20. Original LR

21. Solution Procedure Since there are two decision variable( X jk, Y j ) =>divide into two subproblem

22. Solution Procedure P jk QjQj

23. Solution Procedure After optimally solving each Lagrangean relaxation problem (by subgradient method), a set of decision variables can be found, but may not feasible Propose a heuristic algorithm for obtaining feasible solutions

24. Solution Procedure

27. Computational Results algorithm tested on 10 by 10 sensor area

28. Computational Results algorithm tested on 10 by 10 sensor area

29. Computational Results algorithm tested on 10 by 10 sensor area 0.80 / 3 = 26.7%

30. Computational Results algorithm tested on 10 by 10 sensor area 80 / 40 = 2

31. Computational Results algorithm tested on 10 by 10 sensor area

32. Computational Results algorithm tested on 10 by 10 sensor area The solution time of the algorithm is below 100 seconds in all cases. The efficiency of the algorithm thus can be confirmed.

33. Computational Results algorithm tested on different size of sensor area

34. Conclusion Proposed algorithm is truly novel and it has not been discussed in previous researches Prolong the networking lifetime almost to theoretical upper bound

35. Conclusion My opinion and what I learned here –Algorithm description is too rough –An example to formulate a problem into integer programming –Use Lagangean Relaxation to obtain lower bounds for minimization problems