1. Framing Algorithms for Approximate Multicriteria Shortest Paths
- Author
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Hanusse, Nicolas, Ilcinkas, David, Lentz, Antonin, Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), and ANR-16-CE40-0023,DESCARTES,Abstraction modulaire pour le calcul distribué(2016)
- Subjects
shortest paths ,Applied computing → Multi-criterion optimization and decision-making ,Theory of computation → Shortest paths ,[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS] ,multicriteria ,Pareto set ,approximation - Abstract
This paper deals with the computation of d-dimensional multicriteria shortest paths. In a weighted graph with arc weights represented by vectors, the cost of a path is the vector sum of the weights of its arcs. For a given pair consisting of a source s and a destination t, a path P dominates a path Q if and only if P’s cost is component-wise smaller than or equal to Q’s cost. The set of Pareto paths, or Pareto set, from s to t is the set of paths that are not dominated. The computation time of the Pareto paths can be prohibitive whenever the set of Pareto paths is large. We propose in this article new algorithms to compute approximated Pareto paths in any dimension. For d = 2, we exhibit the first approximation algorithm, called Frame, whose output is guaranteed to be always a subset of the Pareto set. Finally, we provide a small experimental study in order to confirm the relevance of our Frame algorithm., OASIcs, Vol. 85, 20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020), pages 11:1-11:19
- Published
- 2020