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.IPEC.2018.11
URN: urn:nbn:de:0030-drops-102121
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10212/
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Eppstein, David ; Lokshtanov, Daniel

The Parameterized Complexity of Finding Point Sets with Hereditary Properties

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LIPIcs-IPEC-2018-11.pdf (0.4 MB)

Abstract

We consider problems where the input is a set of points in the plane and an integer k, and the task is to find a subset S of the input points of size k such that S satisfies some property. We focus on properties that depend only on the order type of the points and are monotone under point removals. We exhibit a property defined by three forbidden patterns for which finding a k-point subset with the property is W[1]-complete and (assuming the exponential time hypothesis) cannot be solved in time n^{o(k/log k)}. However, we show that problems of this type are fixed-parameter tractable for all properties that include all collinear point sets, properties that exclude at least one convex polygon, and properties defined by a single forbidden pattern.

BibTeX - Entry

@InProceedings{eppstein_et_al:LIPIcs:2019:10212,
  author =	{David Eppstein and Daniel Lokshtanov},
  title =	{{The Parameterized Complexity of Finding Point Sets with Hereditary Properties}},
  booktitle =	{13th International Symposium on Parameterized and Exact  Computation (IPEC 2018)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-084-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{115},
  editor =	{Christophe Paul and Michal Pilipczuk},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10212},
  URN =		{urn:nbn:de:0030-drops-102121},
  doi =		{10.4230/LIPIcs.IPEC.2018.11},
  annote =	{Keywords: parameterized complexity, fixed-parameter tractability, point set pattern matching, largest pattern-avoiding subset, order type}
}

Keywords: parameterized complexity, fixed-parameter tractability, point set pattern matching, largest pattern-avoiding subset, order type
Collection: 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)
Issue Date: 2019
Date of publication: 05.02.2019

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