eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-06-11
40:1
40:16
10.4230/LIPIcs.SoCG.2019.40
article
An Experimental Study of Forbidden Patterns in Geometric Permutations by Combinatorial Lifting
Goaoc, Xavier
1
Holmsen, Andreas
2
Nicaud, Cyril
3
Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Department of Mathematical Sciences, KAIST, Daejeon, South Korea
Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE, UPEM, F-77454, Marne-la-Vallée, France
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol129-socg2019/LIPIcs.SoCG.2019.40/LIPIcs.SoCG.2019.40.pdf
Geometric permutation
Emptiness testing of semi-algebraic sets
Computer-aided proof