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Approximation Algorithms for the Unsplittable Flow Problem on Paths and Trees

Authors: Khaled Elbassioni, Naveen Garg, Divya Gupta, Amit Kumar, Vishal Narula, and Arindam Pal

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)


Abstract
We study the Unsplittable Flow Problem (UFP) and related variants, namely UFP with Bag Constraints and UFP with Rounds, on paths and trees. We provide improved constant factor approximation algorithms for all these problems under the no bottleneck assumption (NBA), which says that the maximum demand for any source-sink pair is at most the minimum capacity of any edge. We obtain these improved results by expressing a feasible solution to a natural LP relaxation of the UFP as a near-convex combination of feasible integral solutions.

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Khaled Elbassioni, Naveen Garg, Divya Gupta, Amit Kumar, Vishal Narula, and Arindam Pal. Approximation Algorithms for the Unsplittable Flow Problem on Paths and Trees. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 267-275, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


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@InProceedings{elbassioni_et_al:LIPIcs.FSTTCS.2012.267,
  author =	{Elbassioni, Khaled and Garg, Naveen and Gupta, Divya and Kumar, Amit and Narula, Vishal and Pal, Arindam},
  title =	{{Approximation Algorithms for the Unsplittable Flow Problem on Paths and Trees}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{267--275},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.267},
  URN =		{urn:nbn:de:0030-drops-38650},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.267},
  annote =	{Keywords: Approximation Algorithms, Integer Decomposition, Linear Programming, Scheduling, Unsplittable Flows}
}
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