Parallel multilevel graph partitioning

In this paper we present a parallel formulation of a graph partitioning and sparse matrix ordering algorithm that is based an a multilevel algorithm we developed recently. Our parallel algorithm achieves a speedup of up to 56 on a 128-processor Cray T3D for moderate size problems, further reducing its already moderate serial run-time. Graphs with over 200,000 vertices can be partitioned in 128 parts, on a 128-processor Gray T3D in less than 3 seconds. This is at least an order of magnitude better than any previously reported run times on 128-processors for obtaining an 128-partition. This also makes it possible to use our parallel graph partitioning algorithm to partition meshes dynamically in adaptive computations. Furthermore, the quality of the produced partitions and orderings are comparable to those produced by the serial multilevel algorithm that has been shown to substantially outperform both spectral partitioning and multiple minimum degree.

[1]  Michael T. Heath,et al.  A Cartesian Parallel Nested Dissection Algorithm , 1992, SIAM J. Matrix Anal. Appl..

[2]  S.,et al.  An Efficient Heuristic Procedure for Partitioning Graphs , 2022 .

[3]  Horst D. Simon,et al.  A Parallel Implementation of Multilevel Recursive Spectral Bisection for Application to Adaptive Unstructured Meshes. Chapter 1 , 1994 .

[4]  Stephen T. Barnard.  PMRSB: Parallel Multilevel Recursive Spectral Bisection , 1995, SC.

[5]  Padma Raghavan,et al.  Parallel Ordering Using Edge Contraction , 1997, Parallel Comput..

[6]  Curt Jones,et al.  A Heuristic for Reducing Fill-In in Sparse Matrix Factorization , 1993, PPSC.

[7]  Thomas J. R. Hughes,et al.  An efficient communications strategy for finite element methods on the Connection Machine CM-5 system , 1994 .

[8]  Bruce Hendrickson,et al.  A Multi-Level Algorithm For Partitioning Graphs , 1995, Proceedings of the IEEE/ACM SC95 Conference.

[9]  Joseph W. H. Liu,et al.  Modification of the minimum-degree algorithm by multiple elimination , 1985, TOMS.

[10]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[11]  Steven J. Plimpton,et al.  Parallel Algorithms for Dynamically Partitioning Unstructured Grids , 1995, PPSC.

[12]  Thomas J. R. Hughes,et al.  Mesh Decomposition and Communication Procedures for Finite Element Applications on the Connection Machine CM-5 System , 1994, HPCN.

[13]  George Karypis,et al.  Introduction to Parallel Computing , 1994 .

[14]  Bruce Hendrickson,et al.  The Chaco user`s guide. Version 1.0 , 1993 .

[15]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[16]  Alan George,et al.  Computer Solution of Large Sparse Positive Definite , 1981 .

[17]  Gary L. Miller,et al.  A unified geometric approach to graph separators , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[18]  Alex Pothen,et al.  PARTITIONING SPARSE MATRICES WITH EIGENVECTORS OF GRAPHS* , 1990 .

[19]  Horst D. Simon,et al.  Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems , 1994, Concurr. Pract. Exp..

[20]  George Karypis,et al.  Multilevel k-way Partitioning Scheme for Irregular Graphs , 1998, J. Parallel Distributed Comput..

[21]  Vipin Kumar,et al.  Analysis of Multilevel Graph Partitioning , 1995, Proceedings of the IEEE/ACM SC95 Conference.