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Triangle width: at the intersection of graph theory, scheduling and matrix visualization

Luc Libralesso 1 Vincent Jost 2 Khadija Hadj Salem 3 Florian Fontan 2 Frédéric Maffray 1
1 G-SCOP_OC - Optimisation Combinatoire
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
2 G-SCOP_ROSP - Recherche Opérationnelle pour les Systèmes de Production
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
Abstract : We introduce a new problem that can be studied from 3 different angles: scheduling, matrix visualization and vertex ordering in hypergraphs. We prove the equivalence of the different formulations of the problem and use them to prove several of its NP-Hard and polynomial subcases. This problem allows to find more elegant (and arguably shorter) proofs for several combinatorial problems. Including "Can a matrix can be made triangular by permuting rows and columns?" and weak k-visit. It also provides an elegant generalization of Johnson's argument for the two-machine flowshop.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03010258
Contributor : Khadija Hadj Salem <>
Submitted on : Tuesday, November 17, 2020 - 4:07:10 PM
Last modification on : Tuesday, February 2, 2021 - 5:28:18 PM
Long-term archiving on: : Thursday, February 18, 2021 - 7:59:42 PM

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  • HAL Id : hal-03010258, version 1

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Luc Libralesso, Vincent Jost, Khadija Hadj Salem, Florian Fontan, Frédéric Maffray. Triangle width: at the intersection of graph theory, scheduling and matrix visualization. inPress. ⟨hal-03010258⟩

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