Fast and E ective Algorithms for Graph Partitioningand Sparse

LIMITED DISTRIBUTION NOTICE This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and speciic requests. After outside publication, requests should be lled only by reprints or legally obtained copies of the article (e.g., payment of royalties). Abstract Graph partitioning is a fundamental problem in several scientiic and engineering applications. In this paper, we describe heuristics that improve the state-of-the-art practical algorithms used in graph-partitioning software in terms of both partitioning speed and quality. An important use of graph-partitioning is in ordering sparse matrices for obtaining direct solutions to sparse systems of linear equations arising in engineering and optimization applications. The experiments reported in this paper show that the use of these heuristics results in a considerable improvement in the quality of sparse-matrix orderings over conventional ordering methods , especially for sparse matrices arising in linear programming problems. In addition, our graph-partitioning-based ordering algorithm is more parallelizable than minimum-degree-based ordering algorithms, and it renders the ordered matrix more amenable to parallel factorization.