Improved Deterministic Algorithms for Linear Programming in Low Dimensions

At SODA’93, Chazelle and Matouˇsek presented a derandomization of Clarkson’s sampling-based algorithm [FOCS’88] 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 Br¨onnimann, Chazelle, and Matouˇsek [FOCS’93]. 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.

• Type: Journal
• Year: 2016
• Where: SODA
• Authors: Timothy M. Chan
• Keywords: Algorithms, SODA 2016