Faster (1+ε)-approximation for unsplittable flow on a path via resource augmentation and back
- 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 giveUnsplittable 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.…
Author: | Fabrizio Grandoni, Tobias MömkeORCiDGND, Andreas Wiese |
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URN: | urn:nbn:de:bvb:384-opus4-1084307 |
Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/108430 |
ISBN: | 978-3-95977-204-4OPAC |
ISSN: | 1868-8969OPAC |
Parent Title (English): | 29th Annual European Symposium on Algorithms (ESA 2021), September 6-8, 2021, online conference |
Publisher: | Schloss Dagstuhl, Leibniz-Zentrum für Informatik |
Place of publication: | Dagstuhl |
Editor: | Petra Mutzel, Rasmus Pagh, Grzegorz Herman |
Type: | Conference Proceeding |
Language: | English |
Year of first Publication: | 2021 |
Publishing Institution: | Universität Augsburg |
Release Date: | 2023/10/17 |
First Page: | 49:1 |
Last Page: | 49:15 |
Series: | Leibniz International Proceedings in Informatics (LIPIcs) ; 204 |
DOI: | https://doi.org/10.4230/LIPIcs.ESA.2021.49 |
Institutes: | Fakultät für Angewandte Informatik |
Fakultät für Angewandte Informatik / Institut für Informatik | |
Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Theoretische Informatik / Resource Aware Algorithmics | |
Dewey Decimal Classification: | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
Licence (German): | CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |