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- W3109062912 abstract "We consider the Max-Cut problem on an undirected graph $$G=(V,E)$$ with $$|V|=n$$ nodes and $$|E|=m$$ edges. We investigate a linear size MIP formulation, referred to as (MIP-MaxCut), which can easily be derived via a standard linearization technique. However, the efficiency of the Branch-and-Bound procedure applied to this formulation does not seem to have been investigated so far in the literature. Branch-and-bound based approaches for Max-Cut usually use the semi-metric polytope which has either an exponential size formulation consisting of the cycle inequalities or a compact size formulation consisting of O(mn) triangle inequalities (Barahona and Mahjoub in Math Prog 36:157–173, 1986; Nguyen and Minoux in Networks 69(1):142–150, 2017). However, optimizing over the semi-metric polytope can be computationally demanding due to the slow convergence of cutting-plane algorithms and the high degeneracy of formulations based on the triangle inequalities. In this paper, we exhibit new structural properties of (MIP-MaxCut) that link the binary variables with the cycle inequalities. In particular, we show that fixing a binary variable at 0 or 1 in (MIP-MaxCut) can result in imposing the integrity of several original variables and the satisfaction of a possibly exponential number of cycle inequalities in the semi-metric formulation. Numerical results show that for sparse instances of Max-Cut, our approach exploiting this capability outperforms the branch-and-cut algorithms based on semi-metric polytope when implemented on the same framework; and even without any extra sophistication, the approach is capable of solving hard instances of Max-Cut within acceptable CPU times." @default.
- W3109062912 created "2020-12-07" @default.
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- W3109062912 date "2020-11-20" @default.
- W3109062912 modified "2023-10-12" @default.
- W3109062912 title "Linear size MIP formulation of Max-Cut: new properties, links with cycle inequalities and computational results" @default.
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- W3109062912 doi "https://doi.org/10.1007/s11590-020-01667-z" @default.
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