On Helly's theorem: Algorithms and extensions

A. Brieden; P. Gritzmann

doi:10.1007/PL00009300

On Helly's theorem: Algorithms and extensions

A. Brieden
, P. Gritzmann

University of Trier

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

This paper studies algorithmic Helly-type problems in the framework of the algorithmic theory of convex bodies developed by Grötschel, Lovász, and Schrijver. Various oracle-polynomial-time algorithms are presented that are complemented by ℕℙ-hardness results for polytopes. In addition, some new Helly-type theorems are derived.

Original language	English
Pages (from-to)	393-410
Number of pages	18
Journal	Discrete and Computational Geometry
Volume	17
Issue number	4
DOIs	https://doi.org/10.1007/PL00009300
State	Published - Jun 1997
Externally published	Yes

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title = "On Helly's theorem: Algorithms and extensions",

abstract = "This paper studies algorithmic Helly-type problems in the framework of the algorithmic theory of convex bodies developed by Gr{\"o}tschel, Lov{\'a}sz, and Schrijver. Various oracle-polynomial-time algorithms are presented that are complemented by ℕℙ-hardness results for polytopes. In addition, some new Helly-type theorems are derived.",

author = "A. Brieden and P. Gritzmann",

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AB - This paper studies algorithmic Helly-type problems in the framework of the algorithmic theory of convex bodies developed by Grötschel, Lovász, and Schrijver. Various oracle-polynomial-time algorithms are presented that are complemented by ℕℙ-hardness results for polytopes. In addition, some new Helly-type theorems are derived.

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DO - 10.1007/PL00009300

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JO - Discrete and Computational Geometry

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ER -

On Helly's theorem: Algorithms and extensions

Abstract

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