Unstructured Graph Partitioning and Sparse Matrix Ordering System
نویسندگان
چکیده
Graph partitioning has extensive applications in many areas, including scientific computing, VLSI design, and task scheduling. The problem is to partition the vertices of a graph in p roughly equal parts, such that the number of edges connecting vertices in different parts is minimized. For example, the solution of a sparse system of linear equations Ax = b via iterative methods on a parallel computer gives rise to a graph partitioning problem. A key step in each iteration of these methods is the multiplication of a sparse matrix and a (dense) vector. Partitioning the graph corresponding to the matrix A, significantly reduces the amount of communication required by this step [25]. If parallel direct methods are used to solve a sparse system of equations, then a graph partitioning algorithm can be used to compute a fill reducing ordering that lead to high degree of concurrency in the factorization phase [25, 10]. The multiple minimum degree ordering used almost exclusively in serial direct methods is not suitable for parallel direct methods, as it provides very little concurrency in the parallel factorization phase. METIS is a set of programs that implement the various algorithms described in [22, 23]. The advantages of METIS compared to other similar packages are the following:
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