Mathematical Programming

, Volume 44, Issue 1, pp 203-212

First online:

A randomized algorithm for fixed-dimensional linear programming

  • M. E. DyerAffiliated withUniversity of Leeds
  • , A. M. FriezeAffiliated withCarnegie-Mellon UniversityQueen Mary College

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We give a (Las Vegas) randomized algorithm for linear programming in a fixed dimensiond for which the expected computation time is\(O(d^{(3 + \varepsilon _d )d} n)\), where lim d→∞ ε d = 0. This improves the corresponding worst-case complexity,\(O(3^{d^2 } n)\). The method is based on a recent idea of Clarkson. Two variations on the algorithm are examined briefly.

Key words

Linear programming randomized algorithm