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DOI: 10.4230/LIPIcs.IPEC.2018.11
URN: urn:nbn:de:0030-drops-102121
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10212/
Eppstein, David ; Lokshtanov, Daniel
The Parameterized Complexity of Finding Point Sets with Hereditary Properties
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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 | |
| Seminar: | 13th International Symposium on Parameterized and Exact Computation (IPEC 2018) | |
| Issue date: | 2019 | |
| Date of publication: | 05.02.2019 |
