A combinatorial bound for linear programming and related problems

  • Micha Sharir
  • Emo Welzl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)


We present a simple randomized algorithm which solves linear programs with n constraints and d variables in expected O(d32 d n) 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.


computational geometry combinatorial optimization linear programming randomized incremental algorithms 


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Copyright information

© Springer-Verlag Berlin Heidelberg 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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