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

The paper presents a Coarse-Grained Multicomputer algorithm that solves the problem of finding the longest repeated su#x ending at each point in a word. This algorithm can be implemented in the CGM with P processors in O( )intimeandO(P ) communication steps. It is the first CGM algorithm for this problem. We present also experimental results showing that the CGM algorithm is very e#cient.