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DOI: 10.4230/LIPIcs.MFCS.2016.35

Preprocessing Under Uncertainty: Matroid Intersection

Authors: Stefan Fafianie, Eva-Maria C. Hols, Stefan Kratsch, and Vuong Anh Quyen

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract

We continue the study of preprocessing under uncertainty that was initiated independently by Assadi et al. (FSTTCS 2015) and Fafianie et al. (STACS 2016). Here, we are given an instance of a tractable problem with a large static/known part and a small part that is dynamic/uncertain, and ask if there is an efficient algorithm that computes an instance of size polynomial in the uncertain part of the input, from which we can extract an optimal solution to the original instance for all (usually exponentially many) instantiations of the uncertain part. In the present work, we focus on the Matroid Intersection problem. Amongst others we present a positive preprocessing result for the important case of finding a largest common independent set in two linear matroids. Motivated by an application for intersecting two gammoids we also revisit Maximum Flow. There we tighten a lower bound of Assadi et al. and give an alternative positive result for the case of low uncertain capacity that yields a Maximum Flow instance as output rather than a matrix.

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Stefan Fafianie, Eva-Maria C. Hols, Stefan Kratsch, and Vuong Anh Quyen. Preprocessing Under Uncertainty: Matroid Intersection. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{fafianie_et_al:LIPIcs.MFCS.2016.35,
  author =	{Fafianie, Stefan and Hols, Eva-Maria C. and Kratsch, Stefan and Quyen, Vuong Anh},
  title =	{{Preprocessing Under Uncertainty: Matroid Intersection}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{35:1--35:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.35},
  URN =		{urn:nbn:de:0030-drops-64490},
  doi =		{10.4230/LIPIcs.MFCS.2016.35},
  annote =	{Keywords: preprocessing, uncertainty, maximum flow, matroid intersection}
}

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Preprocessing Under Uncertainty: Matroid Intersection

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