A branch-and-cut algorithm for the equicut problem

Abstract

We describe an algorithm for solving the equicut problem on complete graphs. The core of the algorithm is a cutting-plane procedure that exploits a subset of the linear inequalities defining the convex hull of the incidence vectors of the edge sets that define an equicut. The cuts are generated by several separation procedures that will be described in the paper. Whenever the cutting-plane procedure does not terminate with an optimal solution the algorithm uses a branch-and-cut strategy. We also describe the implementation of the algorithm and the interface with the LP solver. We then report on our computational results.

Multicommodity Flow Approximation Used for Exact Graph Partitioning

“…In most works on exact graph partitioning (see e.g. [2,18]), sets like Random and RandW are used for the experiments. We added the sets of random regular and random planar graphs here, because we believe that more structured graph classes should also be considered with respect to their bigger relevance for practical applications.…”

“…This modified length function does not change the analysis but it is reported that the algorithm behaves better 2 We write Ç £ to denote the "smooth" O-calculus hiding logarithmic factors. 3 A full version of this paper including all proofs can be found in [30].…”

“…In [6], Ferreira et al present a branch-and-cut algorithm for the problem. The same approach is followed by L. Brunetta, M. Conforti, and G. Rinaldi in [2]. In [15], E. Johnson, A. Mehrotra, and G. Nemhauser elaborate on a column generation approach for the graph partitioning problem.…”

High quality graph partitioning

“…This includes methods dedicated to the bipartitioning case [32,93,64,153,11,12,50,52,63] and some methods that solve the general graph partitioning problem [65,154]. Most of the methods rely on the branch-and-bound framework [106].…”

Solving k-Way Graph Partitioning Problems to Optimality: The Impact of Semidefinite Relaxations and the Bundle Method

“…Alternatively, this latter constraint added to the max-cut problem gives the equicut problem which can be motivated by an application to Coulomb glasses in theoretical physics. Motivated by this application, Anjos et al [5] recently proposed an enhanced branch-and-cut algorithm for equicut based on an approach proposed by Brunetta et al [13].…”