Local Algorithms for Edge Colorings in UDGs

Abstract

In this paper we consider two problems: the edge coloring and the strong edge coloring problems on unit disk graphs (UDGs). Both problems have important applications in wireless sensor networks as they can be used to model link scheduling problems in such networks. It is well known that both problems are NP-complete, and approximation algorithms for them have been extensively studied under the centralized model of computation. Centralized algorithms, however, are not suitable for ad-hoc wireless sensor networks whose devices typically have limited resources, and lack the centralized coordination.

We develop local distributed approximation algorithms for the edge coloring and the strong edge coloring problems on unit disk graphs. For the edge coloring problem, our local distributed algorithm has approximation ratio 2 and locality 50. We show that the locality upper bound can be improved to 28 while keeping the same approximation ratio, at the expense of increasing the computation time at each node. For the strong edge coloring problem on UDGs, we present two local distributed algorithms with different tradeoffs between their approximation ratio and locality. The first algorithm has ratio 128 and locality 22, whereas the second algorithm has ratio 10 and locality 180.