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

This paper addresses the triangle width problem , which generalizes the classic two-machine flexible job-shop problem (FJSP) with tooling constraints. This new problem can be studied from three different angles: scheduling, matrix visualization, and vertex ordering in hypergraphs. We prove the equiv...

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Bibliographic Details
Published inAnnals of operations research Vol. 337; no. 2; pp. 715 - 730
Main Authors Hadj Salem, Khadija, Libralesso, Luc, Jost, Vincent, Fontan, Florian, Maffray, Frédéric
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2024
Springer Nature B.V
Springer Verlag
Subjects
Business and Management
Combinatorial analysis
Combinatorics
Computer Science
Graph theory
Graphs
Mathematics
Operations Research/Decision Theory
Original Research
Scheduling
Theory of Computation
Tooling
Triangles
Visualization
Scheduling
Graph theory
Binary matrix visualization
Combinatorial optimization
Combinatorial Optimization
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Summary:This paper addresses the triangle width problem , which generalizes the classic two-machine flexible job-shop problem (FJSP) with tooling constraints. This new problem can be studied from three 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 establish the N P -Hardness and polynomiality of several of its subcases. This problem allows us to find more elegant (and probably shorter) proofs for several combinatorial problems in our analysis setting. Our study provides an elegant generalization of Johnson’s argument for the two-machine flow shop. It also shows the relation between the question: “Is a matrix triangular?” and the “ k -visit of a graph”.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-024-05890-0