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Journal Articles SIAM Journal on Discrete Mathematics Year : 2015

Tropicalizing the simplex algorithm


We develop a tropical analog 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.

Dates and versions

hal-00930913 , version 1 (14-01-2014)



Xavier Allamigeon, Pascal Benchimol, Stéphane Gaubert, Michael Joswig. Tropicalizing the simplex algorithm. SIAM Journal on Discrete Mathematics, 2015, 29 (2), ⟨10.1137/130936464⟩. ⟨hal-00930913⟩
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