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.
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Acknowledgments
We would like to thank Carlo Mannino for providing the interesting max-cut instances arising in the frequency assignment context and the referees for the careful reading of the paper.
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Bonato, T., Jünger, M., Reinelt, G. et al. Lifting and separation procedures for the cut polytope. Math. Program. 146, 351–378 (2014). https://doi.org/10.1007/s10107-013-0688-2
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DOI: https://doi.org/10.1007/s10107-013-0688-2
Keywords
- Max-cut problem
- Cut polytope
- Separation algorithm
- Branch-and-cut
- Unconstrained boolean quadratic programming
- Ising spin glass model