On Constructing k -Connected k -Dominating Set in Wireless Networks

1. On Constructing k-Connected k-Dominating Set in Wireless Networks Fei Dai and Jie Wu, "On Constructing k-Connected k-Dominating Set in Wireless Networks," in Proc. of 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS 05), 2005. Presented By Donghyun KimMay 21, 2008Mobile Computing and Wireless Networking Research Group at University of Texas at Dallas

2. In simulation, DSR/AODV over virtual backbones performs better than plain DSR/AODV. • By decreasing backbone size • Communication overhead can be reduced. • Increase the convergence speed (in routing). • Simplify the connectivity management. • Provide a backup route. • Support broadcasting or multicasting. • Reduce the overall energy consumption. Virtual Backbone Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

3. Gossip [1] • Each node forwards a message received with probability . • Coverage Condition [2] • Node does node forwards a message between and , if there is a replacement path that connects and via several intermediate nodes (if any) with higher priorities than that of . Background Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

4. -Vertex Connectivity • A network is -vertex connected if it is connected and removing any 1, 2, …, nodes from will not cause partition in . • -Connected -Dominating Set • A node set is a -dominating set (or simply -DS) of if every node not in has at least neighboring nodes in . A -DS is a -connected -dominating set (or simply -CDS) of if the subgraph induced from is -vertex connected. Definitions Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

5. Definitions – cont’ Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

6. Fault tolerant virtual backbone (in terms of…) • Coverage • Connectivity • Computing a -Connected -Dominating Set • Smaller backbone is preferred. • Other considerations? • Energy Efficiency – not yet, so far. • Diameter – not yet, so far. Design Criteria Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

7. Initiate the research regarding fault-tolerant virtual backbone. • Present 3 localized algorithms to compute -connected -dominating sets. • Probabilistic approach • Deterministic approach • A hybrid paradigm • No constant approximation ratio Contribution of This Paper Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

8. -Gossip • Each node has a backbone status with probability . • In -Gossip, the perfect value of which constructs a small virtual backbone while maintaining a -CDS with high probability, depending on following factors • Total node number • Deploy area • Transmission range • -Gossip incurs very low overhead at each node, no information exchange, and computation. • Expected size of a virtual backbone is . Probabilistic Approach Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

9. Probabilistic Approach – cont’ Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

10. -Coverage Condition • Node has a non-backbone status if for any two neighbors and , node disjoint replacement paths exist that connect and via several intermediate nodes (if any) with higher ID’s than . Deterministic Approach Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

11. Lemma 1 • A node set is a -CDS of network if after removing any nodes from , the remaining part of is a CDS of the remaining part of . • Theorem 1 • If the -coverage condition is applied to a -connected network , the resultant virtual backbone forms a -CDS of G. Deterministic Approach – cont’

12. Suppose we have a subset of nodes which is not a CDS. CDS Disconnected DS Insufficient DS Why k-coverage Condition Works? Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

13. Each node selects a random color for itself. As a result, the node set is divided into disjoint subsets , with each subset containing nodes with color . • For each color , a localized CDS algorithm A is applied to construct a virtual backbone that covers the original network. • The final -CDS is the union of all colored virtual backbones. Color-Based k-CDS Construction (CBKC) Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

14. Color-Based k-CDS Construction (CBKC) – Cont’ Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

15. Comparison Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

16. [1] X. Hou and D. Tipper, “Gossip-based sleep protocol (GSP) for energy efficient routing in wireless ad-hoc networks,” in Proc. of WCNC, March 2004. [2] J. Wu and F. Dai, “A generic distributed broadcast scheme in ad hoc wireless networks,” IEEE Transactions on Computers , vol. 53, pp. 1343-1354, Oct. 2004. References Presented by Donghyun Kim on May 21, 2008Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas