Parallel algorithms for approximate edge colouring of simple graphs

Abstract

Two parallel algorithms for edge-colouring simple graphs are presented. One takes O(mlogn) time using a polynomial number of processors on an SIMD parallel computer which allows read conflicts but no write conflicts. The second algorithm uses the first in a divide-and-conquer setting and takes O(nlog2n) time at the cost of a factor of n extra processors on the same model of computation. How to obtain improved time bounds from these algorithms for some special types of graph is also discussed. Either algorithm uses no more than φe+1 colours where φe is the edge-chromatic number of the graph being coloured. Moreover the expected performance of each of the algorithms is optimal.