A combinatorial bound for linear programming and related problems

  • Micha Sharir
  • Emo Welzl
Conference paper

DOI: 10.1007/3-540-55210-3_213

Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)
Cite this paper as:
Sharir M., Welzl E. (1992) A combinatorial bound for linear programming and related problems. In: Finkel A., Jantzen M. (eds) STACS 92. STACS 1992. Lecture Notes in Computer Science, vol 577. Springer, Berlin, Heidelberg

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.

Keywords

computational geometry combinatorial optimization linear programming randomized incremental algorithms 

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Micha Sharir
    • 1
    • 2
  • Emo Welzl
    • 3
  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  3. 3.Institut für InformatikFreie Universität BerlinBerlin 33Germany

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