eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-08-31
49:1
49:15
10.4230/LIPIcs.ESA.2021.49
article
Faster (1+ε)-Approximation for Unsplittable Flow on a Path via Resource Augmentation and Back
Grandoni, Fabrizio
1
Mömke, Tobias
2
https://orcid.org/0000-0002-2509-6972
Wiese, Andreas
3
IDSIA, USI-SUPSI, Lugano, Switzerland
Department of Computer Science, Universität Augsburg, Germany
Department of Industrial Engineering, Universidad de Chile, Santiago, Chile
Unsplittable flow on a path (UFP) is an important and well-studied problem. We are given a path with capacities on its edges, and a set of tasks where for each task we are given a demand, a subpath, and a weight. The goal is to select the set of tasks of maximum total weight whose total demands do not exceed the capacity on any edge. UFP admits an (1+ε)-approximation with a running time of n^{O_{ε}(poly(log n))}, i.e., a QPTAS {[}Bansal et al., STOC 2006; Batra et al., SODA 2015{]} and it is considered an important open problem to construct a PTAS. To this end, in a series of papers polynomial time approximation algorithms have been developed, which culminated in a (5/3+ε)-approximation {[}Grandoni et al., STOC 2018{]} and very recently an approximation ratio of (1+1/(e+1)+ε) < 1.269 {[}Grandoni et al., 2020{]}. In this paper, we address the search for a PTAS from a different angle: we present a faster (1+ε)-approximation with a running time of only n^{O_{ε}(log log n)}. We first give such a result in the relaxed setting of resource augmentation and then transform it to an algorithm without resource augmentation. For this, we present a framework which transforms algorithms for (a slight generalization of) UFP under resource augmentation in a black-box manner into algorithms for UFP without resource augmentation, with only negligible loss.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol204-esa2021/LIPIcs.ESA.2021.49/LIPIcs.ESA.2021.49.pdf
Approximation Algorithms
Unsplittable Flow
Dynamic Programming