The Tropical Double Description Method

Allamigeon, Xavier; Gaubert, Stéphane; Goubault, Éric

doi:10.4230/LIPIcs.STACS.2010.2443

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The Tropical Double Description Method

Authors Xavier Allamigeon, Stéphane Gaubert, Éric Goubault

Part of: Volume: 27th International Symposium on Theoretical Aspects of Computer Science (STACS 2010)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
License: Creative Commons Attribution-NoDerivs 3.0 Unported license
Publication Date: 2010-03-09

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Document Identifiers

DOI: 10.4230/LIPIcs.STACS.2010.2443
URN: urn:nbn:de:0030-drops-24435

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Keywords

Convexity in tropical algebra
algorithmics and combinatorics of tropical polyhedra
computational geometry
discrete event systems
static analysis

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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.

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Xavier Allamigeon, Stéphane Gaubert, and Éric Goubault. The Tropical Double Description Method. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 47-58, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010) https://doi.org/10.4230/LIPIcs.STACS.2010.2443

Author Details

Xavier Allamigeon

Stéphane Gaubert

Éric Goubault

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