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.APPROX-RANDOM.2017.6
URN: urn:nbn:de:0030-drops-75559
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7555/
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Goemans, Michel X. ; Unda, Francisco

Approximating Incremental Combinatorial Optimization Problems

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LIPIcs-APPROX-RANDOM-2017-6.pdf (0.5 MB)

Abstract

We consider incremental combinatorial optimization problems, in which a solution is constructed incrementally over time, and the goal is to optimize not the value of the final solution but the average value over all timesteps. We consider a natural algorithm of moving towards a global optimum solution as quickly as possible. We show that this algorithm provides an approximation guarantee of (9+sqrt(21))/15 > 0.9 for a large class of incremental combinatorial optimization problems defined axiomatically, which includes (bipartite and non-bipartite) matchings, matroid intersections, and stable sets in claw-free graphs. Furthermore, our analysis is tight.

BibTeX - Entry

@InProceedings{goemans_et_al:LIPIcs:2017:7555,
  author =	{Michel X. Goemans and Francisco Unda},
  title =	{{Approximating Incremental Combinatorial Optimization Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7555},
  URN =		{urn:nbn:de:0030-drops-75559},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.6},
  annote =	{Keywords: Approximation algorithm, matching, incremental problems, matroid intersection, integral polytopes, stable sets}
}

Keywords: Approximation algorithm, matching, incremental problems, matroid intersection, integral polytopes, stable sets
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Issue Date: 2017
Date of publication: 11.08.2017

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