Alessandro Panconesi, Romeo Rizzi

2001, Note: Published in Distributed Computing, vol. 14 (2001) 97-100

Keywords: distributed computing, sparse networks, maximal independent set, maximal matching, vertex colouring, edge colouring

Abstract:We give simple, deterministic, distributed algorithms for computing maximal matchings, maximal independent sets and colourings. We show that edge colourings with at most 2D-1 colours, and maximal matchings can be computed within O(log^* n + D) deterministic rounds, where D is the maximum degree of the network. We also show how to find maximal independent sets and (D+1)-vertex colourings within O(log^* n + D^2) deterministic rounds. All hidden constants are very small and the algorithms are very simple.