A Faster Distributed Approximation Scheme for the Connected Dominating Set Problem for Growth-Bounded Graphs
نویسندگان
چکیده
We present a distributed algorithm for finding a (1 + ε)approximation of a Minimum Connected Dominating Set in the class of Growth-Bounded graphs, which includes Unit Disk graphs. In addition, the computed Connected Dominating Set guarantees a constant stretch factor on the length of a shortest path with respect to the original graph and induces a subgraph of constant degree. The nodes do not require any positioning or distance information. The algorithm runs in O ` TMIS + 1/ε O(1) · log∗ n ́ synchronous rounds, where TMIS is the time for computing a Maximal Independent Set (MIS) in the network graph. Using the fastest known deterministic algorithm for computing a MIS, the total running time is O ` (log∆ + 1/ε) · log∗ n ́ , where ∆ is the maximum degree of the network graph. If one allows randomization, the running time reduces to O ` (log logn+ 1/ε) · log∗ n ́
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