Scalable, Shared Memory Parallel Graph Coloring Heuristics

Assefaw Hadish Gebremedhin and Fredrik Manne

Reports in Informatics No. 181, December 1999, Department of Informatics, University of Bergen, Norway.


Finding a good graph coloring quickly is often a crucial phase in the development of efficient, parallel algorithms for many scientific 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 finite element methods and eigen value computations validate the theoretical run-time analysis.