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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10444/
Goaoc, Xavier ;
Holmsen, Andreas ;
Nicaud, Cyril
An Experimental Study of Forbidden Patterns in Geometric Permutations by Combinatorial Lifting
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}
}
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Keywords: |
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Geometric permutation, Emptiness testing of semi-algebraic sets, Computer-aided proof |
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Collection: |
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35th International Symposium on Computational Geometry (SoCG 2019) |
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Issue Date: |
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2019 |
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Date of publication: |
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11.06.2019 |
