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Article Dans Une Revue Journal of Combinatorial Optimization Année : 2018

On the m-clique free interval subgraphs polytope: polyhedral analysis and applications

Résumé

In this paper we study the m-clique free interval subgraphs. We investigate the facial structure of the polytope defined as the convex hull of the incidence vectors associated with these subgraphs. We also present some facet-defining inequalities to strengthen the associated linear relaxation. As an application, the generalized open-shop problem with disjunctive constraints (GOSDC) is considered. Indeed, by a projection on a set of variables, the m-clique free interval subgraphs represent the solution of an integer linear program solving the GOSDC presented in this paper. Moreover, we propose exact and heuristic separation algorithms, which are exploited into a Branch-and-cut algorithm for solving the GOSDC. Finally, we present and discuss some computational results.
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Dates et versions

hal-03939452 , version 1 (14-01-2023)

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Mohammed-Albarra Hassan, Imed Kacem, Sébastien Martin, Izzeldin Osman. On the m-clique free interval subgraphs polytope: polyhedral analysis and applications. Journal of Combinatorial Optimization, 2018, 36 (3), pp.1074-1101. ⟨10.1007/s10878-018-0291-9⟩. ⟨hal-03939452⟩
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