Scalable, Shared Memory Parallel Graph Coloring Heuristics

Finding a good graph coloring quickly is often a crucial phase in the development of eecient, parallel algorithms for many scientiic and engineering applications. In this paper we consider the problem of solving the graph coloring problem itself in parallel. We present a simple and fast parallel graph coloring heuristic that is well suited for shared memory programming and yields an almost linear speedup on the PRAM model. We also present a second heuristic that improves on the number of colors used. The heuristics have been implemented using OpenMP. Experiments conducted on an SGI Cray Origin 2000 using very large graphs from nite element methods and eigen value computations validate the theoretical run-time analysis.