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Minimum Connected Dominating Set Using a Collaborative Cover Heuristic for Ad Hoc Sensor Networks
March 2010 (vol. 21 no. 3)
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).

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Index Terms:
Connected dominating set (CDS), Steiner tree, routing backbone, maximal independent set (MIS).
Rajiv Misra, Chittaranjan Mandal, "Minimum Connected Dominating Set Using a Collaborative Cover Heuristic for Ad Hoc Sensor Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 21, no. 3, pp. 292-302, March 2010, doi:10.1109/TPDS.2009.78
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