1. Worst and Best-Case Coverage in Sensor Networks Seapahn Meguerdichian, Farinaz Koushanfar, Miodrag Potkonjak, Mani Srivastava IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL.4, NO. 1, JANUARY-FEBRUARY 2005

2. Outline Application Scenarios Problem Formulation Centralized Algorithm Simulation Results

3. Application Scenarios 1. A postman soldier wants to travel a path from I to F over a region distributed mines such that the path walked is far from any mine to minimize the risk. 2. A postman soldier wants to travel a path from I to F over a region protected by allied forces such that the maximum distance of the postman soldier from allied forces is minimized.

4. Problem Formulation (1/2) Breach : Given a path P connecting areas I and F, breach is defined as the minimum Euclidean distance from P to any sensor in S. ( P 距離 sensors 最短距離 ) Worst-Case Coverage Maximal Breach Path Identify a path P from I to F such that P ’ s breach is maximized.

5. Problem Formulation (2/2) Support : Given a path P connecting areas I and F, Support is defined as the maximum Euclidean distance from P to the closest sensor in S. ( P 距離 sensor 最遠距離 ) Best-Case Coverage Minimal Support Path Identify a path P from I to F such that P ’ s support is minimized.

6. Centralized Algorithms Worst-Case Coverage Theorem 1. At least one Maximal Breach Path must lie on the line segments of the bounded Voronoi diagram formed by the locations of the sensors in S.

7. Construction Of Voronoi Diagram Divide-and-Conquer Paradigm [Go Details]Go Details

8. Incremental Method

9. Construction of Voronoi Diagram

11. Maximal Breach Path

12. Complexity Voronoi diagram construction ~  ( n log n ) Breath-first Search ~  (V+E) Voronoi vertices <= 2n-5 Voronoi edges <=3n-6 Binary Search ~  (log range ) range = (max_weight-min_weight)/2 Total:  ( n log range )

13. Centralized Algorithms Best-Case Coverage Theorem 2. At least one Minimal Support Path must lie on the edges of the Delaunay triangulation.

14. Proof

15. Minimal Support Path Algorithm support_weight support_weight = support_weight + range support_weight = support_weight - range

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