ILP-based Local Search for Graph Partitioning

TL;DR

This paper introduces a scalable ILP-based local search heuristic for balanced graph partitioning, significantly improving solutions in benchmark tests by combining integer linear programming with heuristic techniques.

Contribution

It presents a novel scalable ILP-based meta-heuristic that improves graph partitioning solutions by adapting small models with symmetry breaking techniques.

Findings

Improved roughly half of benchmark entries with many blocks.

Scalable approach effective on large inputs.

Enhances existing partitioning solutions.

Abstract

Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that solve the partitioning problem to optimality. However, since those programs typically do not scale to large inputs, we adapt them to heuristically improve a given partition. We do so by defining a much smaller model that allows us to use symmetry breaking and other techniques that make the approach scalable. For example, in Walshaw's well-known benchmark tables we are able to improve roughly half of all entries when the number of blocks is high.