The Weighted Arborescence Constraint

Houndji, Vinasétan Ratheil; Schaus, Pierre; Hounkonnou, Mahouton Norbert; Wolsey, Laurence A.

doi:10.1007/978-3-319-59776-8_15

Cited by 1 publication

(2 citation statements)

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“…We extend the classic connectivity constraints for the MCA [22] in such a way to take precedences into account. When considering a set S ⊆ V \{r} we add a constraint for each j ∈ S, and we force that at least one active arc must enter S coming from the set of vertices allowed to precede j on the path connecting j to r.…”

Section: A Set-based Modelmentioning

confidence: 99%

“…Constraints (21) enforce that the waiting time at vertex j is greater than or equal to the difference between the time at which the flow enters vertex j and the time at which the flow enters vertex i plus c ij . Constraints (22) enforce that the time at which the flow enters vertex t is greater than or equal to the time at which the flow enters vertex s for all (s, t) ∈ R. Finally, constraints ( 23) and ( 24) define the domain of the variables. The MILP model proposed, without constraints (18), has O(|A|) variables, and O(|A|) constraints.…”

Section: A Distance-accumulation Modelmentioning

confidence: 99%

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Precedence-Constrained Arborescences

Chou¹,

Dell’Amico²,

Jamal³

et al. 2022

Preprint

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The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different objective function and/or constraints. Recently, the Precedence-Constrained Minimum-Cost Arborescence problem was proposed, in which precedence constraints are enforced on pairs of vertices. These constraints prevent the formation of directed paths that violate precedence relationships along the tree. We show that this problem is NP-hard, and we introduce a new scalable mixed integer linear programming model for it. With respect to the previous models, the newly proposed model performs substantially better. This work also introduces a new variation on the minimum-cost arborescence problem with precedence constraints. We show that this new variation is also NP-hard, and we propose several mixed integer linear programming models for formulating the problem.

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Section: A Set-based Modelmentioning

confidence: 99%

Section: A Distance-accumulation Modelmentioning

confidence: 99%