On the Quadratic Shortest Path Problem - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2015

On the Quadratic Shortest Path Problem

Abstract

Finding the shortest path in a directed graph is one of the most important combinatorial optimization problems, having applications in a wide range of fields. In its basic version, however, the problem fails to represent situations in which the value of the objective function is determined not only by the choice of each single arc, but also by the combined presence of pairs of arcs in the solution. In this paper we model these situations as a Quadratic Shortest Path Problem, which calls for the minimization of a quadratic objective function subject to shortest-path constraints. We prove strong NP-hardness of the problem and analyze polynomially solvable special cases, obtained by restricting the distance of arc pairs in the graph that appear jointly in a quadratic monomial of the objective function. Based on this special case and problem structure, we devise fast lower bounding procedures for the general problem and show computationally that they clearly outperform other approaches proposed in the literature in terms of its strength.
Fichier principal
Vignette du fichier
QSPPaperHal.pdf (323.12 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01251438 , version 1 (06-01-2016)

Identifiers

Cite

Borzou Rostami, Federico Malucelli, Davide Frey, Christoph Buchheim. On the Quadratic Shortest Path Problem. 14th International Symposium on Experimental Algorithms, Jun 2015, Paris, France. ⟨10.1007/978-3-319-20086-6_29⟩. ⟨hal-01251438⟩
417 View
780 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More