License: Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2010.2443
URN: urn:nbn:de:0030-drops-24435
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2010/2443/
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Allamigeon, Xavier ; Gaubert, Stéphane ; Goubault, Éric

The Tropical Double Description Method

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Abstract

We develop a tropical analogue of the classical double description method allowing one to compute an internal representation (in terms of vertices) of a polyhedron defined externally (by inequalities). The heart of the tropical algorithm is a characterization of the extreme points of a polyhedron in terms of a system of constraints which define it. We show that checking the extremality of a point reduces to checking whether there is only one minimal strongly connected component in an hypergraph. The latter problem can be solved in almost linear time, which allows us to eliminate quickly redundant generators. We report extensive tests (including benchmarks from an application to static analysis) showing that the method outperforms experimentally the previous ones by orders of magnitude. The present tools also lead to worst case bounds which improve the ones provided by previous methods.

BibTeX - Entry

@InProceedings{allamigeon_et_al:LIPIcs:2010:2443,
  author =	{Xavier Allamigeon and St{\'e}phane Gaubert and {\'E}ric Goubault},
  title =	{{The Tropical Double Description Method}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{47--58},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Jean-Yves Marion and Thomas Schwentick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2443},
  URN =		{urn:nbn:de:0030-drops-24435},
  doi =		{10.4230/LIPIcs.STACS.2010.2443},
  annote =	{Keywords: Convexity in tropical algebra, algorithmics and combinatorics of tropical polyhedra, computational geometry, discrete event systems, static analysis}
}

Keywords: Convexity in tropical algebra, algorithmics and combinatorics of tropical polyhedra, computational geometry, discrete event systems, static analysis
Collection: 27th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2010
Date of publication: 09.03.2010

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