A distributed algorithm to find k-dominating sets Original Research Article

We consider a connected undirected graph G(n,m) with n nodes and m edges. A k-dominating set D in G is a set of nodes having the property that every node in G is at most k edges away from at least one node in D. Finding a k-dominating set of minimum size is NP-hard. We give a new synchronous distributed algorithm to find a k-dominating set in G of size no greater than ⌊n/(k+1)⌋. Our algorithm requires O(k log∗ n) time and O(m log k+n log k log∗ n) messages to run. It has the same time complexity as the best currently known algorithm, but improves on that algorithmʹs message complexity and is, in addition, conceptually simpler.