1. Tropical determinant on transportation polytopes.
- Author
-
Gajula, Sailaja, Soprunov, Ivan, and Soprunova, Jenya
- Subjects
- *
LINEAR programming , *POLYTOPES , *MATHEMATICAL optimization , *BIRKHOFF'S theorem (Relativity) , *NUMERICAL analysis , *MATHEMATICAL models - Abstract
Let D k , l ( m , n ) be the set of all the integer points in the transportation polytope of k n × l n matrices with row sums lm and column sums km . In this paper we find the sharp lower bound on the tropical determinant over the set D k , l ( m , n ) . This integer piecewise linear programming problem in arbitrary dimension turns out to be equivalent to an integer non-linear (in fact, quadratic) optimization problem in dimension two. We also compute the sharp upper bound on a modification of the tropical determinant, where the maximum over all the transversals in a matrix is replaced with the minimum. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF