A combinatorial bound for linear programming and related problems

Micha Sharir, Emo Welzl

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We present a simple randomized algorithm which solves linear programs with n constraints and d variables in expected O(d32dn) time. The expectation is over the internal randomizations performed by the algorithm, and holds for any input. The algorithm is presented in an abstract framework, which facilitates its application to a large class of problems, including computing smallest enclosing balls (or ellipsoids) of finite point sets in d-space, computing largest balls (ellipsoids) in convex polytopes, convex programming in general, etc.

Original languageEnglish
Title of host publicationSTACS 1992 - 9th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings
EditorsAlain Finkel, Matthias Jantzen
PublisherSpringer Verlag
Pages569-579
Number of pages11
ISBN (Print)9783540552109
DOIs
StatePublished - 1992
Event9th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1992 - Cachan, France
Duration: 13 Feb 199215 Feb 1992

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume577 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference9th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1992
Country/TerritoryFrance
CityCachan
Period13/02/9215/02/92

Funding

FundersFunder number
Israeli Academy of Sciences
Office of Naval l~searehN00014-O0-J-1284
U.S.-Israeli Binational Science Foundation
National Science FoundationCCR-89-01484
European Society for Philosophy and Psychology
European Commission3075

    Keywords

    • Combinatorial optimization
    • Computational geometry
    • Linear programming
    • Randomized incremental algorithms

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