TY - GEN

T1 - A combinatorial bound for linear programming and related problems

AU - Sharir, Micha

AU - Welzl, Emo

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1992.

PY - 1992

Y1 - 1992

N2 - 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.

AB - 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.

KW - Combinatorial optimization

KW - Computational geometry

KW - Linear programming

KW - Randomized incremental algorithms

UR - http://www.scopus.com/inward/record.url?scp=84990629463&partnerID=8YFLogxK

U2 - 10.1007/3-540-55210-3_213

DO - 10.1007/3-540-55210-3_213

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84990629463

SN - 9783540552109

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 569

EP - 579

BT - STACS 1992 - 9th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings

A2 - Finkel, Alain

A2 - Jantzen, Matthias

PB - Springer Verlag

T2 - 9th Annual Symposium on Theoretical Aspects of Computer Science, STACS 1992

Y2 - 13 February 1992 through 15 February 1992

ER -