Improved Deterministic Algorithms for Linear Programming in Low Dimensions

Author:

CHAN Timothy M.1

Affiliation:

1. University of Illinois at Urbana-Champaign,IL, USA

Abstract

Chazelle and Matoušek [ J. Algorithms , 1996] presented a derandomization of Clarkson’s sampling-based algorithm [ J. ACM , 1995] for solving linear programs with n constraints and d variables in d (7+ o (1)) d n deterministic time. The time bound can be improved to d (5+ o (1)) d n with subsequent work by Brönnimann, Chazelle, and Matoušek [ SIAM J. Comput. , 1999]. We first point out a much simpler derandomization of Clarkson’s algorithm that avoids ε-approximations and runs in d (3+ o (1)) d n time. We then describe a few additional ideas that eventually improve the deterministic time bound to d (1/2+ o (1)) d n .

Publisher

Association for Computing Machinery (ACM)

Subject

Mathematics (miscellaneous)

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