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Pré-Publication, Document De Travail Année : 2023

Hard Problems In Box-Totally Dual Integral Polyhedra

Résumé

In this paper, we study the complexity of some fundamental questions regarding box-totally dual integral (box-TDI) polyhedra. First, although box-TDI polyhedra have strong integrality properties, we prove that Integer Programming over box-TDI polyhedra is NP-complete, that is, finding an integer point optimizing a linear function over a box-TDI polyhedron is hard. Second, we complement the result of Ding et al. [10] who proved that deciding whether a given system is box-TDI is co-NPcomplete: we prove that recognizing whether a polyhedron is box-TDI is co-NP-complete. To derive these complexity results, we exhibit new classes of totally equimodular matrices-a generalization of totally unimodular matrices-by characterizing the total equimodularity of incidence matrices of graphs.
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hal-03932335 , version 1 (23-01-2023)

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  • HAL Id : hal-03932335 , version 1

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Patrick Chervet, Roland Grappe, Mathieu Lacroix, Francesco Pisanu, Roberto Wolfler Calvo. Hard Problems In Box-Totally Dual Integral Polyhedra. 2023. ⟨hal-03932335⟩
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