Distributed Approximation of Capacitated Dominating Sets

We study local, distributed algorithms for the capacitated minimum dominating set (CapMDS) problem, which arises in various distributed network applications. Given a network graph G = (V, E), and a capacity cap(v) N for each node v V , the CapMDS problem asks for a subset S V of minimal cardinality, such that every network node not in S is covered by at least one neighbor in S, and every node v S covers at most cap(v) of its neighbors. We prove that in general graphs and even with uniform capacities, the problem is inherently non-local, i.e., every distributed algorithm achieving a non-trivial approximation ratio must have a time complexity that essentially grows linearly with the network diameter. On the other hand, if for some parameter > 0, capacities can be violated by a factor of 1 + , CapMDS becomes much more local. Particularly, based on a novel distributed randomized rounding technique, we present a distributed bi-criteria algorithm that achieves an O(log )-approximatio...

• Type: Journal
• Year: 2010
• Where: MST
• Authors: Fabian Kuhn, Thomas Moscibroda
• Keywords: Algorithms, Graph Theory, Hardware, MST 2010, Network Graphs