Polyhedral Computations for the Simple Graph Partitioning Problem

The simple graph partitioning problem is to partition an edge-weighted graph into mutually disjoint subgraphs, each containing no more than b nodes, such that the sum of the weights of all edges in the subgraphs is maximal. In this paper we present a branch-and-cut algorithm for the problem that uses several classes of facet-defining inequalities as cuttingplanes. These are b-tree, clique, cycle with ear, multistar, and S, Tinequalities. Descriptions of the separation procedures that are used for these inequality classes are also given. In order to evaluate the usefulness of the inequalities and the overall performance of the branch-and-cut algorithm several computational experiments are conducted. We present some of the results of these experiments.Branch-and-cut algorithm; Facets; Graph partitioning; Multicuts; Separation procedures

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

On the bridge between combinatorial optimization and nonlinear optimization: a family of semidefinite bounds for 0-1 quadratic problems leading to quasi-Newton methods

International audienceThis article presents a family of semidefinite programming bounds, obtained by Lagrangian duality, for 0-1 quadratic optimization problems with linear or quadratic constraints. These bounds have useful computational properties: they have a good ratio of tightness to computing time, they can be optimized by a quasi-Newton method, and their final tightness level is controlled by a real parameter. These properties are illustrated on three standard combinatorial optimization problems: unconstrained 0-1 quadratic optimization, heaviest k-subgraph, and graph bisection