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.SoCG.2019.40
URN: urn:nbn:de:0030-drops-104442
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10444/
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Goaoc, Xavier ; Holmsen, Andreas ; Nicaud, Cyril

An Experimental Study of Forbidden Patterns in Geometric Permutations by Combinatorial Lifting

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LIPIcs-SoCG-2019-40.pdf (0.7 MB)


Abstract

We study the problem of deciding if a given triple of permutations can be realized as geometric permutations of disjoint convex sets in R^3. We show that this question, which is equivalent to deciding the emptiness of certain semi-algebraic sets bounded by cubic polynomials, can be "lifted" to a purely combinatorial problem. We propose an effective algorithm for that problem, and use it to gain new insights into the structure of geometric permutations.

BibTeX - Entry

@InProceedings{goaoc_et_al:LIPIcs:2019:10444,
  author =	{Xavier Goaoc and Andreas Holmsen and Cyril Nicaud},
  title =	{{An Experimental Study of Forbidden Patterns in Geometric Permutations by Combinatorial Lifting}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{40:1--40:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10444},
  URN =		{urn:nbn:de:0030-drops-104442},
  doi =		{10.4230/LIPIcs.SoCG.2019.40},
  annote =	{Keywords: Geometric permutation, Emptiness testing of semi-algebraic sets, Computer-aided proof}
}

Keywords: Geometric permutation, Emptiness testing of semi-algebraic sets, Computer-aided proof
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019


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