1. The Coverage Problem in Wireless Ad Hoc Sensor Networks Supervisor: Prof. Sanjay Srivastava By, Rucha Kulkarni 200811039

2. Outline Introduction Types of coverage. Computational Geometry Background Study Algorithm for coverage calculation Open problems

3. Introduction Sensor node is equipped with: –Sensing range –Communication range Issues in sensor networks: –Location discovery –Tracking –Deployment –Coverage Coverage: Measure of Quality of Service –How well a region is covered? –What is the probability that an object will be detected? –K-coverage

4. Types of Coverage Blanket coverage Barrier coverage Point coverage Path coverage Exposure Fig.1 Blanket coverage Fig.2 Barrier coverage Fig.3 Point coverage

5. Computational Geometry Voronoi diagrams Delaunay triangulations Voronoi DiagramDelaunay triangulation

6. Background Study [2] studies the k-coverage of wireless sensor networks [3] studies about the node deployment mechanisms [6] presents a mechanism to find paths with minimum exposure [9] derives a relationship between coverage and connectivity and integrates CCP and SPAN to guarantee coverage with connectivity

7. Worst Case Coverage Given: A field deployed with sensors; areas I and F Problem: Find a maximal breach path P b from I to F P b is the path such that every point on the path is at least breach_weight away from the sensors. Assumptions: –Deterministic deployment of sensors –Sensing ability decreases with increase in distance

8. Algorithm Construct the voronoi diagram for the given set of sensor nodes Construct a graph from the voronoi diagram: –Each vertex in the voronoi diagram corresponds to a node in the graph –Each line segment in the voronoi diagram corresponds to an edge in the graph –Each edge is assigned weight equal to the minimum distance from the closest sensor node. Binary search is used to find the smallest and the largest edge in the graph using breach_weight as the threshold value During each iteration, BFS is used to check for the existence of a path from I to F

9. Best case coverage Given: A field deployed with sensors; areas I and F Problem: Find a maximal support path P s from I to F P s is the path such that distance between every point on the path the sensors is minimized. Assumptions: –Deterministic deployment of sensors –Sensing ability decreases with increase in distance

10. Algorithm The algorithm for the best case coverage calculation is same as for the worst case coverage with some changes: –The voronoi diagram is replaced with Delaunay triangulation; –The edges in the graph are assigned weights equal to the lengths of the Delaunay lines; –The breach_weight is replaced by the support_weight.

11. Open Problems To design an algorithm for the deployment of the sensor nodes to obtain the desired coverage with minimal energy consumption Coverage in three dimensional spaces Barrier coverage problem

12. References [1] M. Cardei and J. Wu, “Coverage in Wireless Sensor Networks," Handbook of Sensor networks, CRC Press, 2004. [2] C.-F. Huang and Y.-C. Tseng, “The coverage problem in a wireless sensor networks,“ ACM International Workshop on Wireless Sensor Networks and Applications (WSNA), 2003, pp. 115-121. [3] K. Kar and S. Banerjee, “Node Placement for Connected Coverage in Sensor Networks,“ Proceedings of WiOpt 2003: Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, March 2003. [4] B. Liu, D. Towsley, “On the coverage and detectability of large-scale wireless sensor networks," Proceedings of the Modeling and Optimization in Mobile, Ad hoc and Wireless Networks Conference (WiOpt). (2003) [5] S. Meguerdichian, F. Koushanfar, M. Potkonjak, M. Srivastava, “Coverage problems in Wireless Add-Hoc Sensor Networks," Proceedings of IEEE Infocom, vol. 3, pp. 1380-1387, April 2001.

13. References (contd.) [6] S. Meguerdichian, F. Koushanfar, G. Qu, and M. Potkonjak, “Exposure in wireless ad-hoc sensor network," ACM Mobile Computing and Networking, pages 139-150, 2001. [7] M.P. Singh; M.M. Gore, “A solution to sensor network coverage problem", Proceedings of 7th IEEE International Conference on Personal Wireless Communication (ICPWC 2005), Jan. 2005, pp.77-80. [8] Sasa Slijepcevic, Miodrag Potkonjak, “Power Efficient Organization of Wireless Sensor Networks", IEEE International Conference on Communications, Helsinki, Finland,June 2001. [9] X. Wan G. Xing, Y. Zhang, C. Lu. R. Pless. and C. Gill, “Integrated Coverage and Connectivity Configuration in Wireless Sensor Network," First ACM conference on Embedded Networked Sensor Systems (Sen- Sys'03), Los Angeles. CA, November 2003. [10] Ming-Chen Zhao, Jiyain Lei, Min-You Wu, Yunhuai Liu, Wei Shu, “Surface coverage in wireless sensor networks," Proceedings of 28th conference on Computer communications, IEEE Infocom 2009, pp. 109- 117.

14. Thank You