We present an efficient and scalable Coarse Grained Multicomputer (CGM) coloring algorithm that colors a graph G with at most D+ 1 colors where D is the maximum degree in G. This algorithm is given in two variants: randomized and deterministic. We show that on a p-processor CGM model the proposed algorithms require a parallel time of O( |G| p ) and a total work and overall communication cost of O(|G|). These bounds correspond to the average case for the randomized version and to the worst-case for the deterministic variant. Key words: graph algorithms, parallel algorithms, graph coloring, Coarse Grained Multicomputers 1

We discover a surprising connection between graph coloring in two orthogonal paradigms: parallel and on-line computing. We present a randomized on-line coloring algorithm with a performance ratio of O(n = log n), an improvement of plog n factor over the previous best known algorithm of Vishwanathan. Also, from the same principles, we construct a parallel coloring algorithm with the same performance ratio, for the o/rst such result. As a byproduct, we obtain a parallel approximation for the independent set problem.