License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.59
URN: urn:nbn:de:0030-drops-90638
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9063/
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Garg, Shashwat

Quasi-PTAS for Scheduling with Precedences using LP Hierarchies

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LIPIcs-ICALP-2018-59.pdf (0.5 MB)


Abstract

A central problem in scheduling is to schedule n unit size jobs with precedence constraints on m identical machines so as to minimize the makespan. For m=3, it is not even known if the problem is NP-hard and this is one of the last open problems from the book of Garey and Johnson. We show that for fixed m and epsilon, {polylog}(n) rounds of Sherali-Adams hierarchy applied to a natural LP of the problem provides a (1+epsilon)-approximation algorithm running in quasi-polynomial time. This improves over the recent result of Levey and Rothvoss, who used r=(log n)^{O(log log n)} rounds of Sherali-Adams in order to get a (1+epsilon)-approximation algorithm with a running time of n^O(r).

BibTeX - Entry

@InProceedings{garg:LIPIcs:2018:9063,
  author =	{Shashwat Garg},
  title =	{{Quasi-PTAS for Scheduling with Precedences using LP Hierarchies}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{59:1--59:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9063},
  URN =		{urn:nbn:de:0030-drops-90638},
  doi =		{10.4230/LIPIcs.ICALP.2018.59},
  annote =	{Keywords: Approximation algorithms, hierarchies, scheduling, rounding techniques}
}

Keywords: Approximation algorithms, hierarchies, scheduling, rounding techniques
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018


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