Parallel and on-line graph coloring algorithms

Abstract

We discover a surprising connection between graph coloring algorithms in two orthogonal paradigms: parallel and on-line computing. We present a randomized on-line coloring algorithm with a performance guarantee of O(n/logn), an improvement of √logn factor. Also, from the same principle, we construct a parallel coloring Mgorithm with the same performance guarantee, for the first such result. Fina]ly, we show how to apply the parallel algorithm to obtain an NC approximation algorithm for the independent set problem.