Improved linearized models for graph partitioning problem under capacity constraints

Abstract

We investigate a variant of the Graph Partitioning Problem with capacity constraints imposed on the clusters, giving rise to quadratic constraints in 0-1 formulations. Several compact linearized models of the problem are proposed and analyzed: a) a model featuring O(n 3) binary variables which results from the application of the standard Fortet linearization technique; b) a more compact model featuring only O(n 2) binary variables, obtained by linearization after reformulation of the quadratic constraints as bilinear constraints; c) a strengthened version of the latter model, still featuring O(n 2) variables. Computational experiments comparing the relative strength and efficiency of the various models on a series of test instances involving complete graphs with up to 50 nodes are reported and discussed.