A Comparison of Parallel Graph Coloring Algorithms

Dynamic irregular triangulated meshes are used in adaptive grid partial di erential equation (PDE) solvers, and in simulations of random surface models of quantum gravity in physics and cell membranes in biology. Parallel algorithms for random surface simulations and adaptive grid PDE solvers require coloring of the triangulated mesh, so that neighboring vertices are not updated simultaneously. Graph coloring is also used in iterative parallel algorithms for solving large irregular sparse matrix equations. Here we introduce some parallel graph coloring algorithms based on well-known sequential heuristic algorithms, and compare them with some existing parallel algorithms. These algorithms are implemented on both SIMD and MIMD parallel architectures and tested for speed, e ciency, and quality (the average number of colors required) for coloring random triangulated meshes and graphs from sparse matrix problems.