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Issue No. 03 - March (2010 vol. 21)
ISSN: 1045-9219
pp: 292-302
Rajiv Misra , Indian Institute of Technology, Patna
Chittaranjan Mandal , Indian Institute of Technology, Kharagpur
A minimum connected dominating set (MCDS) is used as virtual backbone for efficient routing and broadcasting in ad hoc sensor networks. The minimum CDS problem is NP-complete even in unit disk graphs. Many heuristics-based distributed approximation algorithms for MCDS problems are reported and the best known performance ratio has (4.8+\ln 5). We propose a new heuristic called collaborative cover using two principles: 1) domatic number of a connected graph is at least two and 2) optimal substructure defined as subset of independent dominator preferably with a common connector. We obtain a partial Steiner tree during the construction of the independent set (dominators). A final postprocessing step identifies the Steiner nodes in the formation of Steiner tree for the independent set of G. We show that our collaborative cover heuristics are better than degree-based heuristics in identifying independent set and Steiner tree. While our distributed approximation CDS algorithm achieves the performance ratio of (4.8+\ln 5){\rm opt} + 1.2, where {\rm opt} is the size of any optimal CDS, we also show that the collaborative cover heuristic is able to give a marginally better bound when the distribution of sensor nodes is uniform permitting identification of the optimal substructures. We show that the message complexity of our algorithm is O(n\Delta^{2} ), \Delta being the maximum degree of a node in graph and the time complexity is O(n).
Connected dominating set (CDS), Steiner tree, routing backbone, maximal independent set (MIS).

C. Mandal and R. Misra, "Minimum Connected Dominating Set Using a Collaborative Cover Heuristic for Ad Hoc Sensor Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 21, no. , pp. 292-302, 2009.
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