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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.6

Approximating Incremental Combinatorial Optimization Problems

Authors: Michel X. Goemans and Francisco Unda

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

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.

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Michel X. Goemans and Francisco Unda. Approximating Incremental Combinatorial Optimization Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{goemans_et_al:LIPIcs.APPROX-RANDOM.2017.6,
  author =	{Goemans, Michel X. and Unda, Francisco},
  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 =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.6},
  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}
}

@InProceedings{goemans_et_al:LIPIcs.APPROX-RANDOM.2017.6,
  author =	{Goemans, Michel X. and Unda, Francisco},
  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 =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.6},
  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}
}

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Approximating Incremental Combinatorial Optimization Problems

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