Parallelism in graph-partitioning

Abstract

Graph partitioning is an important NP-complete problem with applications in VLSI CAD, processor allocation, and many other areas. The problem is to partition vertices of a graph into two equal-sized sets so that the number of edges joining the sets is minimum. In this paper we show that the Kernighan-Lin heuristic is P-complete and the simulated annealing heuristic is P-hard, which suggests that they are both hard to parallelize. We also describe a new parallel heuristic (which we call the Mob heuristic) that on the 32K-processor CM-2 Connection Machine handles graphs with more than two million edges and gives in 9-min partitions that are within 2% of the best ever found. © 1991.