Mathematical Programming

, Volume 146, Issue 1, pp 351–378

Lifting and separation procedures for the cut polytope

  • Thorsten Bonato
  • Michael Jünger
  • Gerhard Reinelt
  • Giovanni Rinaldi
Full Length Paper Series A

DOI: 10.1007/s10107-013-0688-2

Cite this article as:
Bonato, T., Jünger, M., Reinelt, G. et al. Math. Program. (2014) 146: 351. doi:10.1007/s10107-013-0688-2

Abstract

The max-cut problem and the associated cut polytope on complete graphs have been extensively studied over the last 25 years. However, in comparison, only little research has been conducted for the cut polytope on arbitrary graphs, in particular separation algorithms have received only little attention. In this study we describe new separation and lifting procedures for the cut polytope on general graphs. These procedures exploit algorithmic and structural results known for the cut polytope on complete graphs to generate valid, and sometimes facet defining, inequalities for the cut polytope on arbitrary graphs in a cutting plane framework. We report computational results on a set of well-established benchmark problems.

Keywords

Max-cut problem Cut polytope Separation algorithm  Branch-and-cut Unconstrained boolean quadratic programming   Ising spin glass model 

Mathematics Subject Classification (2000)

90C27 90C57 90C20 90C09 82D30 

Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2013

Authors and Affiliations

  • Thorsten Bonato
    • 1
  • Michael Jünger
    • 2
  • Gerhard Reinelt
    • 1
  • Giovanni Rinaldi
    • 3
  1. 1.Institut für InformatikUniversität HeidelbergHeidelbergGermany
  2. 2.Institut für InformatikUniversität zu KölnCologneGermany
  3. 3.Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, CNRRomeItaly