Tropicalizing the Simplex Algorithm
Abstract
We develop a tropical analogue of the simplex algorithm for linear programming. In particular, we obtain a combinatorial algorithm to perform one tropical pivoting step, including the computation of reduced costs, in $O(n(m+n))$ time, where $m$ is the number of constraints and $n$ is the dimension.
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© 2015, Society for Industrial and Applied Mathematics.
History
Submitted: 10 September 2013
Accepted: 3 November 2014
Published online: 16 April 2015
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