Think Locally, Act Globally: Perfectly Balanced Graph Partitioning

Abstract: We present a novel local improvement scheme for the perfectly balanced graph partitioning problem. This scheme encodes local searches that are not restricted to a balance constraint into a model allowing us to find combinations of these searches maintaining balance by applying a negative cycle detection algorithm. We combine this technique with an algorithm to balance unbalanced solutions and integrate it into a parallel multi-level evolutionary algorithm, KaFFPaE, to tackle the problem. Overall, we obtain a system that is fast on the one hand and on the other hand is able to improve or reproduce most of the best known perfectly balanced partitioning results ever reported in the literature.