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

Engineering Branch-and-Cut Algorithms for the Equicut Problem

A minimum equicut of an edge-weighted graph is a partition of the nodes of the graph into two sets of equal size such hat the sum of the weights of edges joining nodes in different partitions is minimum. We compare basic linear and semidefnite relaxations for the equicut problem, and and that linear bounds are competitive with the corresponding semidefnite ones but can be computed much faster. Motivated by an application of equicut in theoretical physics, we revisit an approach by Brunetta et al. and present an enhanced branch-and-cut algorithm. Our computational results suggest that the proposed branch-andcut algorithm has a better performance than the algorithm of Brunetta et al.. Further, it is able to solve to optimality in reasonable time several instances with more than 200 nodes from the physics application

Sonet Network Design Problems

This paper presents a new method and a constraint-based objective function to solve two problems related to the design of optical telecommunication networks, namely the Synchronous Optical Network Ring Assignment Problem (SRAP) and the Intra-ring Synchronous Optical Network Design Problem (IDP). These network topology problems can be represented as a graph partitioning with capacity constraints as shown in previous works. We present here a new objective function and a new local search algorithm to solve these problems. Experiments conducted in Comet allow us to compare our method to previous ones and show that we obtain better results

Recent Advances in Graph Partitioning

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