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Documents authored by Pal, Arindam

Document
DOI: 10.4230/LIPIcs.FSTTCS.2012.199
Scheduling Resources for Executing a Partial Set of Jobs

Authors: Venkatesan T. Chakaravarthy, Arindam Pal, Sambuddha Roy, and Yogish Sabharwal

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

Abstract
In this paper, we consider the problem of choosing a minimum cost set of resources for executing a specified set of jobs. Each input job is an interval, determined by its start-time and end-time. Each resource is also an interval determined by its start-time and end-time; moreover, every resource has a capacity and a cost associated with it. We consider two versions of this problem. In the partial covering version, we are also given as input a number k, specifying the number of jobs that must be performed. The goal is to choose $k$ jobs and find a minimum cost set of resources to perform the chosen k jobs (at any point of time the capacity of the chosen set of resources should be sufficient to execute the jobs active at that time). We present an O(log n)-factor approximation algorithm for this problem. We also consider the prize collecting version, wherein every job also has a penalty associated with it. The feasible solution consists of a subset of the jobs, and a set of resources, to perform the chosen subset of jobs. The goal is to find a feasible solution that minimizes the sum of the costs of the selected resources and the penalties of the jobs that are not selected. We present a constant factor approximation algorithm for this problem.
Cite as

Venkatesan T. Chakaravarthy, Arindam Pal, Sambuddha Roy, and Yogish Sabharwal. Scheduling Resources for Executing a Partial Set of Jobs. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 199-210, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{chakaravarthy_et_al:LIPIcs.FSTTCS.2012.199,
  author =	{Chakaravarthy, Venkatesan T. and Pal, Arindam and Roy, Sambuddha and Sabharwal, Yogish},
  title =	{{Scheduling Resources for Executing a Partial Set of Jobs}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{199--210},
  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.2012.199},
  URN =		{urn:nbn:de:0030-drops-38598},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.199},
  annote =	{Keywords: Approximation Algorithms, Partial Covering, Interval Graphs}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2012.267
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.
Cite as

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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