A distributed algorithm for k-dominating sets

This paper presents a fast distributed algorithm to find a small fe-dominating set in a graph G, with n nodes and m edges, n > k + 1. A k-dominating set D of G is a set of nodes such that for every node υ of G, there exists a node of D whose distance to υ is at most k. D is said to be a small k-dominating set if it has at most [n/k+1] nodes, which is the best lower bound for the size of D in general. The algorithm is synchronous, its time complexity is O(klog ∗n) and its message complexity is O(n log k log∗ n). Small k-dominating sets have applications in a number of areas, including the design of distributed data structures, the selection of servers in a network, and routing with sparse tables. Note, finally, that the decision problem related to finding the smallest k-dominating set of G is NP-Complete.