2026-07-22T20:50:17Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14630 2024-03-06T10:54:29Z ddc:004 open_access

Faster (1+ε)-Approximation for Unsplittable Flow on a Path via Resource Augmentation and Back Grandoni, Fabrizio Mömke, Tobias Wiese, Andreas Approximation Algorithms Unsplittable Flow Dynamic Programming 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Fabrizio Grandoni and Tobias Mömke and Andreas Wiese 2021 Is Part Of LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2021.49 urn:nbn:de:0030-drops-146301 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.49 eng https://creativecommons.org/licenses/by/4.0/legalcode