Unsplittable Flow on a Short Path

Ilan Doron-Arad, Fabrizio Grandoni, Ariel Kulik

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In the Unsplittable Flow on a Path problem (UFP), we are given a path graph with edge capacities and a collection of tasks. Each task is characterized by a demand, a profit, and a subpath. Our goal is to select a maximum profit subset of tasks such that the total demand of the selected tasks that use each edge e is at most the capacity of e. BagUFP is the generalization of UFP where tasks are partitioned into bags, and we are allowed to select at most one task per bag. UFP admits a PTAS [Grandoni,Mömke,Wiese’22] but not an EPTAS [Wiese’17]. BagUFP is APX-hard [Spieksma’99] and the current best approximation is O(log n/log log n) [Grandoni,Ingala,Uniyal’15], where n is the number of tasks. In this paper, we study the mentioned two problems when parameterized by the number m of edges in the graph, with the goal of designing faster parameterized approximation algorithms. We present a parameterized EPTAS for BagUFP, and a substantially faster parameterized EPTAS for UFP (which is an FPTAS for m = O(1)). We also show that a parameterized FPTAS for UFP (hence for BagUFP) does not exist, therefore our results are qualitatively tight.

Original languageEnglish
Title of host publication19th International Symposium on Parameterized and Exact Computation, IPEC 2024
EditorsEdouard Bonnet, Pawel Rzazewski
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959773539
DOIs
StatePublished - 5 Dec 2024
Externally publishedYes
Event19th International Symposium on Parameterized and Exact Computation, IPEC 2024 - London, United Kingdom
Duration: 4 Sep 20246 Sep 2024

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume321
ISSN (Print)1868-8969

Conference

Conference19th International Symposium on Parameterized and Exact Computation, IPEC 2024
Country/TerritoryUnited Kingdom
CityLondon
Period4/09/246/09/24

Keywords

  • Approximation Schemes
  • Knapsack
  • Parameterized Approximations

ASJC Scopus subject areas

  • Software

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