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

Outline

Application Scenarios Problem Formulation Centralized Algorithm Simulation Results

Application Scenarios1. 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.

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.

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.

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.

Construction Of Voronoi Diagram

Divide-and-Conquer Paradigm

[Go Details]

Incremental Method

Construction of Voronoi Diagram

Maximal Breach Path

Complexity Voronoi diagram construction ~ (nlogn) Breath-first Search ~ (V+E)

Voronoi vertices <= 2n-5 Voronoi edges <=3n-6

Binary Search ~ (logrange) range = (max_weight-min_weight)/2

Total: (nlogrange)

Centralized AlgorithmsBest-Case Coverage Theorem 2.

At least one Minimal Support Path must lie on the edges of the Delaunay triangulation.

Proof

Minimal Support Path Algorithm

support_weight

support_weight = support_weight + range

support_weight = support_weight - range

[back]