A Distributed Algorithm for Minimum Distance-k Domination in Trees

Abstract

While efficient algorithms for finding minimal distance-k dominating sets exist, finding minimum such sets is NP-hard even for bipartite graphs. This paper presents a distributed algorithm to determine a minimum (connected) distance-k dominating set and a maximum distance-2k independent set of a tree T. It terminates in O(height(T)) rounds and uses O(logk) space. To the best of our knowledge this is the first distributed algorithm that computes a minimum (as opposed to a minimal) distance-k dominating set for trees. The algorithm can also be applied to general graphs, albeit the distance-k dominating sets are not necessarily minimal.