An efficient parallel algorithm for edge-coloring of graphs

Given G=(V,E) is a simple planar graph, and it doesn´t contain any odd loops, |V|=n, |E|=m. We propose an efficient parallel algorithm for edge-coloring by using /spl Delta/ colors, based on SIMD-CRCW PRAM, a kind of shared memory model that many processors can read and write a unit simultaneously. Here, /spl Delta/ is the maximum degree of vertices of G. If /spl Delta/ is an even number, the algorithm requires O(log/spl Deltaspl middot/log/sup 2/n) time and O(n/spl Delta/) processors; otherwise it requires O(log/spl Deltaspl middot/log/sup 2/n+/spl Deltasup 2/n) time and O(n/spl Delta/) processors. When /spl Delta/=O(log/sup O(1/)n), the algorithm is an efficient algorithm.<>