Graph Domination, Coloring and Cliques in Telecommunications

Abstract

This paper aims to provide a detailed survey of existing graph mod- els and algorithms for important problems that arise in different areas of wireless telecommunication. In particular, applications of graph op- timization problems such as minimum dominating set, minimum vertex coloring and maximum clique in multihop wireless networks are discussed. Different forms of graph domination have been used extensively to model clustering in wireless ad hoc networks. Graph coloring problems and their variants have been used to model channel assignment and scheduling type problems in wireless networks. Cliques are used to derive bounds on chro- matic number, and are used in models of traffic flow, resource allocation, interference, etc. In this paper we survey the solution methods proposed in the literature for these problems and some recent theoretical results that are relevant to this area of research in wireless networks.