2-Connected Relay Placement Problem (2CRPP) in Wireless Sensor Networks

1. 2-Connected Relay Placement Problem (2CRPP) in Wireless Sensor Networks Wei-Lun Wang and Solomon Wu Department of Computer Science and Information Engineering, National Chi Nan University, Puli, Nantou, Taiwan

2. Server Sensor Relay

3. R 1 Sensor Relay What’s RPP • Problem Definition • Input • On an Euclidean plane, given a set of N sensors, which have the effective communication range 1, and a fixed number R ≥ 2, which is the effective communication range of a relay. • Output • To place a minimum number of relays so that between every pair of sensors, s1 and s2, there exists a path P through k relays, r1, r2, …,and rk, such that P=s1r1r2…rks2, d(s1, r1)≦1, d(s2, rk)≦1, andd(ri , rj)≦R, 1≦i< j≦k.

4. Mathematical Facts about RPP BAD • Comparison of the amount of used relaysBAD : WISE : • Assume N=1000, D=2, and R=4.The required number of relays for the first approach is approximately 80919; however, the second approach only needs 1080 relays. That is to say, people who adopt the first approach to deploy relays must spend nearly 75 times higher cost than those who choose the second approach. WISE

5. Approximation Algorithms for RPP • NP-hardRPP is proved to be an NP–hard problem. That is, it is unlikely to find a polynomial-time algorithm which returns the optimal solution. • Many approximation algorithms with different ratios for RPP were proposed to return approximate solutions. • Approximation Ratio Comparisons

6. A F D C E B Sensor Relay Sensor Relay A F D C E B G 2CRPP • Single Point of Failure (SPOF)Failure of a single relay will disconnect the network. • 2CRPPRelays have to be formed as a 2-connected network, that is, there exist at leasttwo disjoint paths between any two relays.

7. Previous Work • Approximation Ratio Comparisons– q is the number of cells in each row of the sensing area While q is a large number, the ratio is close to 8. – M is the maximum node degree of a Minimum Spanning Tree Since M is 5 for Euclidean plan, the ratio is 10. • We then propose a (4+ε)-approximation algorithm for 2CRPP.

8. 1 Sensor Relay (R1) (4+ε)-Approximation Algorithm • Step 1.Place a set of relays R1 by using the Minimum Geometric Disk Cover (MGDC) scheme, such that all sensors are covered by relays.

9. Portal Relay (R1) (4+ε)-Approximation Algorithm • Step 2.Apply R1 to be the input nodes of Traveling Salesman Problem (TSP) to find a Hamiltonian cycle with approximately least cost. Dynamic Programming (X,Y,Z): the shortest path cost X: a square Y: an even portal subset in X Z: a valid pairing

10. R R Relay (R2) Relay (R1) (4+ε)-Approximation Algorithm • Step 3.For each edge e of the Hamiltonian cycle in Step 2, uniformly place relays on it. Let relays which are added here be the set R2.

11. Sensor Relay (R2) Relay (R1) (4+ε)-Approximation Algorithm • Complete the (4+ε)-approximation algorithm. R1∪R2 is a solution of 2CRPP.

12. Conclusion & Future Work • We proposed a (4+ε)-approximation algorithm for solving 2CRPP. When ε is approachingzero, our algorithm will generate a solution with cost which is guaranteed to be less than or equal to 4 times of the optimal solution. • Verify the performance by real implementation, and test them with simulation tools such as Super Sensor Wizard (SSW) and the Network Simulation 2 (NS2). • To further reduce the cost of deploying Smart Grid, better approximation algorithms for 2CRPP with smaller ratios are still desired. Thank You ~