1. / 24 1 Deploying Wireless Sensors to Achieve Both Coverage and Connectivity Xiaole Bai Santosh Kumar Dong Xuan Computer Science and Engineering The Ohio State University MobiHoc 2006

2. / 24 2 Outline Introduction Deployment Model Assumptions and Definitions Proof of Optimality Conclusion

3. / 24 3 Motivations Consideration of coverage alone is no longer enough Having a wireless sensor network just 1-connected is not much useful in practice

4. / 24 4 Goal To design and prove the asymptotic optimality of both coverage and 2-connectivity for all values of r c /r s

5. / 24 5 Deployment Model (Strip-based deployment ) connective a b

6. / 24 6 Regular Deployment Hexagon Square RhombusTriangular

7. / 24 7 Assumptions Both the sensing and communication ranges are regular disks All sensors have the same communication and sensing ranges

8. / 24 8 Definitions (1) : The sensing disk of node u : The communication disk of node u : The distance between node u and v Area Per Node (APN) : The area of the vonoroi cell per node

9. / 24 9 Definitions (2) Connected Neighboring Sensors : The sensing disks of node u and v are intersected l : Minimum length of connection chord φ: Minimum angle of connection angle uv Sensing disk Connection chord Connection angle

10. / 24 10 Optimal deployed number of nodes Evaluate A k,2, k>2 – Regular polygon – Semi-regular polygon Evaluate number of deployed nodes

11. / 24 11 A k,2 uv Sensing disk Connection chord Connection angle Regular Polygon Semi-regular Polygon

12. / 24 12 A k,2 (regular polygon) b a

13. / 24 13 A k,2 (semi-regular polygon) b φ a

14. / 24 14 A k,2 k = 6

15. / 24 15 Different Regular Deployment Patterns Hexagon Square Rhombus Equilateral triangle

16. / 24 16 Maximum APN For The Hexagon-Based Topology ab p

17. / 24 17 Maximum APN For Different Patterns

18. / 24 18 Maximum APN For The Rhombus-Based Topology d bc a θ θ = 90° Square topology d(a, c) ≤ r c Triangle topology ( θ ≤ 60 ° )

19. / 24 19 Maximum APN For The Rhombus-Based Topology

20. / 24 20 Maximum APN

21. / 24 21 The Proof of

22. / 24 22 Compare Different Patterns with Optimal

23. / 24 23 Conclusion A strip-based deployment pattern to achieve coverage and 2-connectivity, and proved its optimality Established the efficiency of popular regular patterns of deployment

24. / 24 24 Thank You !