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 Kim May 21, Mobile Computing and Wireless Networking Research Group
at University of Texas at Dallas

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

3. Background Gossip [1] Coverage Condition [2]
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 .
Presented by Donghyun Kim on May 21, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

4. Definitions -Vertex Connectivity -Connected -Dominating Set
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.
Presented by Donghyun Kim on May 21, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

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

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

7. Contribution of This Paper
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
Presented by Donghyun Kim on May 21, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

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

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

10. Deterministic Approach
-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 .
Presented by Donghyun Kim on May 21, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas

11. Deterministic Approach – cont’
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.

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

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

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

16. References
[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 [2] J. Wu and F. Dai, “A generic distributed broadcast scheme in ad hoc wireless networks,” IEEE Transactions on Computers , vol. 53, pp , Oct
Presented by Donghyun Kim on May 21, 2008 Mobile Computing and Wireless Networking Research Group at The University of Texas at Dallas