In this paper, we present and study a class of graph partitioning algorithms that reduces the size of the graph by collapsing vertices and edges, we find ak-way partitioning of the smaller graph, and then we uncoarsen and refine it to construct ak-way partitioning for the original graph. These algorithms compute ak-way partitioning of a graphG= (V,E) inO(E) time, which is faster by a factor ofO(logk) than previously proposed multilevel recursive bisection algorithms. A key contribution of our work is in finding a high-quality and computationally inexpensive refinement algorithm that can improve upon an initialk-way partitioning. We also study the effectiveness of the overall scheme for a variety of coarsening schemes. We present experimental results on a large number of graphs arising in various domains including finite element methods, linear programming, VLSI, and transportation. Our experiments show that this new scheme produces partitions that are of comparable or better quality than those produced by the multilevel bisection algorithm and requires substantially smaller time. Graphs containing up to 450,000 vertices and 3,300,000 edges can be partitioned in 256 domains in less than 40 s on a workstation such as SGI's Challenge. Compared with the widely used multilevel spectral bisection algorithm, our new algorithm is usually two orders of magnitude faster and produces partitions with substantially smaller edge-cut.
Bibliographical noteFunding Information:
1This work was supported by NSF CCR-9423082, by the Army Research Office Contract DA/DAAH04-95-1-0538, by the IBM Partnership Award, and by the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory Cooperative Agreement Number DAAH04-95-2-0003/Contract DAAH04-95-C-0008, the content of which does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred. Access to computing facilities was provided by AHPCRC, Minnesota Supercomputer Institute, Cray Research Inc., and the Pittsburgh Supercomputing Center. Related papers are available via WWW at URL: http://www.cs.umn.edu/∼karypis. 2E-mail: email@example.com. 3E-mail: firstname.lastname@example.org.
- Graph partitioning; multilevel partitioning methods; Kernighan-Lin heuristic; spectral partitioning methods; parallel sparse matrix algorithms.