In this paper, we study the problem of distributed virtual backbone construction in sensor networks, where the coverage area of nodes are disks with different radii. This problem is modeled by the construction of a minimum connected dominating set (MCDS) in geometric k-disk graphs. We derive the size relationship of any maximal independent set (MIS) and MCDS in geometric k-disk graphs, and apply it to analyze the performances of two distributed connected dominating set (CDS) algorithms we propose in this paper. These algorithms have bounded performance ratio and low communication overhead. To the best of our knowledge, the results reported in this paper represent the state-of-the-art.
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