A faster distributed approximation scheme for the connected dominating set problem for growth-bounded graphs

We present a distributed algorithm for finding a (1 + epsilon)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(T-MIS + 1/epsilon(O(1))center dot 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 Delta + 1/epsilon(O(1))) center dot log* n), where Delta is the maximum degree of the network graph. If one allows randomization, the running time reduces to O((log log n + 1/epsilon(O(1))) center dot log* n) rounds.