Graph partitioning with the Party library: helpful-sets in practice

Abstract

Graph partitioning is an important subproblem in many applications. To partition a graph into more than two parts, there exist two different commonly used approaches: Either the graph is partitioned directly into the desired amount of partitions or the graph is first split into two partitions that are then further divided recursively. It has been shown that even optimal recursive bisection can lead to solutions "very far from the optimal one". However, for "important graph classes" recursive bisection solutions are known to be "almost always" within a constant factor of the optimal one. Thus, the question arises how good recursive bisection performs in practice. In this paper we describe enhancements to the Party graph partitioning library which is based on the helpful-set bisection heuristic and present results of extensive tests undertaken with it. We thereby compare Party with the two state-of-the art libraries Metis and Jostle using a permutation based evaluation scheme. We show experimentally that there are indeed many cases where a recursive application of a good bisection heuristic is likely to find better solutions than up-to-date direct approaches.