Graph coloring on coarse grained multicomputers

We present an efficient and scalable coarse grained multicomputer (CGM) coloring algorithm that colors a graph G with at most Δ+1 colors where Δ 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.