eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2020-11-10
11:1
11:19
10.4230/OASIcs.ATMOS.2020.11
article
Framing Algorithms for Approximate Multicriteria Shortest Paths
Hanusse, Nicolas
1
Ilcinkas, David
1
Lentz, Antonin
2
LaBRI, CNRS & Université Bordeaux, France
LaBRI, Université Bordeaux, France
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.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol085-atmos2020/OASIcs.ATMOS.2020.11/OASIcs.ATMOS.2020.11.pdf
Pareto set
multicriteria
shortest paths
approximation