In this paper, we present CGMgraph, the first integrated library of parallel graph methods for PCclu8(T9 based on CGM algo rithms. CGMgraph implements parallel methods for variou graph prob lems. Ou implementations of deterministic list ranking, Eu er tou- con nected components, spanning forest, and bipartite graph detection are, to ou r knowledge, the first e#cient implementations for PC clu sters.Ou library also inclu des CGMlib, a library of basic CGM tools su ch as sort ing, prefix su m, one to all broadcast, all to one gather, h Relation, all to all broadcast, array balancing, and CGM partitioning. Both libraries are available for download at http://cgm.dehne.net. 1

We present the first efficient algorithm for a coarse grained multiprocessor that colors a graph G with a guarantee of at most D G +1 colors. 1

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

This paper describes efficient coarse-grained parallel algorithms and implementations for a suite of interval graph problems. Included are algorithms requiring only a constant number of communication rounds for connected components, maximum weighted clique, and breadth-first-search and depth-first-search trees, as well as O(log p) communication rounds algorithms for optimization problems such as minimum interval covering, maximum independent set and minimum dominating set, where p is the number of processors in the parallel system. This implies that the number of communication rounds is independent of the problem size. Implementations of these algorithms are evaluated on parallel clusters, using both Fast Ethernet and Myrinet interconnection networks, and on a CRAY T3E parallel multicomputer, with extensive experimental results being presented and analyzed. Copyright # 2002 John Wiley & Sons, Ltd

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