Improved Deterministic Algorithms for Linear Programming in Low Dimensions.

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))dn deterministic time. The time bound can be improved to d(5+o(1))dn 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))dn time. We then describe a few additional ideas that eventually improve the deterministic time bound to d(1/2+o(1))dn.