A Parallel Graph Coloring Heuristic

The problem of computing good graph colorings arises in many diverse applications , such as in the estimation of sparse Jacobians and in the development of eecient, parallel iterative methods for solving sparse linear systems. In this paper we present an asynchronous graph coloring heuristic well suited to distributed memory parallel computers. We present experimental results obtained on an Intel iPSC/860 which demonstrate that, for graphs arising from nite element applications , the heuristic exhibits scalable performance and generates colorings usually within three or four colors of the best-known linear time sequential heuristics. For bounded degree graphs, we show that the expected running time of the heuristic under the PRAM computation model is bounded by EO(log(n)= log log(n)). This bound is an improvement over the previously known best upper bound for the expected running time of a random heuristic for the graph coloring problem.