, Volume 44, Issue 1-3, pp 203-212

A randomized algorithm for fixed-dimensional linear programming

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Abstract

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.