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A combinatorial bound for linear programming and related problems

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STACS 92 (STACS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 577))

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Abstract

We present a simple randomized algorithm which solves linear programs with n constraints and d variables in expected O(d 32d 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.

Work by both authors has been supported by the German-Israeli Foundation for Scientific Research and Development (G.I.F.). Work by the first author has been supported by Office of Naval Research Grant N00014-90-J-1284, by National Science Foundation Grant CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, and the Fund for Basic Research administered by the Israeli Academy of Sciences. Work by the second author has been supported by the ESPRIT II Basic Research Action Program of the EC under contract no. 3075 (project ALCOM).

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Micha Sharir

  2. Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA

    Micha Sharir

  3. Institut für Informatik, Freie Universität Berlin, Arnimallee 2–6, W 1000, Berlin 33, Germany

    Emo Welzl

Authors
  1. Micha Sharir
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  2. Emo Welzl
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Editor information

Alain Finkel Matthias Jantzen

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© 1992 Springer-Verlag Berlin Heidelberg

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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. https://doi.org/10.1007/3-540-55210-3_213

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  • DOI: https://doi.org/10.1007/3-540-55210-3_213

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55210-9

  • Online ISBN: 978-3-540-46775-5

  • eBook Packages: Springer Book Archive

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