Coloring for distributed-memory-parallel Gauss-Seidel algorithm

Abstract

Gauss-Seidel is a well-known iterative method for solving linear system of equations. The computations performed on Gauss-Seidel sweeps are sequential in nature since each component of new iterations depends on previously computed results. Graph coloring is widely used for extracting parallelism in Gauss-Seidel by eliminating data dependencies caused by precedence in the calculations. In this thesis, we present a method to provide a better coloring for distributed-memoryparallel Gauss-Seidel algorithm. Our method utilizes combinatorial approaches including graph partitioning and balanced graph coloring in order to decrease the number of colors while maintaining a computational load balance among the color classes. Experiments performed on irregular sparse problems arising from various scientific applications show that our model effectively reduces the required number of colors thus the number of parallel sweeps in the Gauss-Seidel algorithm.