/ 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

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

/ 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

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

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

/ 24 6 Regular Deployment Hexagon Square RhombusTriangular

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

/ 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

/ 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

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

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

/ A k,2 (regular polygon) b a

/ A k,2 (semi-regular polygon) b φ a

/ A k,2 k = 6

/ Different Regular Deployment Patterns Hexagon Square Rhombus Equilateral triangle

/ Maximum APN For The Hexagon-Based Topology ab p

/ Maximum APN For Different Patterns

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

/ Maximum APN For The Rhombus-Based Topology

/ Maximum APN

/ The Proof of

/ Compare Different Patterns with Optimal

/ 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

/ Thank You !