Tropical determinant on transportation polytope
Sailaja Gajula, Ivan Soprunov, and Jenya Soprunova

TL;DR
This paper establishes the exact lower and upper bounds for the tropical determinant on a specific set of integer matrices within transportation polytopes, linking a complex piecewise-linear problem to a simpler quadratic optimization.
Contribution
It provides the first sharp bounds for the tropical determinant on transportation polytope integer points, connecting high-dimensional linear programming to a 2D quadratic problem.
Findings
Sharp lower bound on tropical determinant established
Sharp upper bound on modified tropical determinant computed
Reduction of a high-dimensional problem to a 2D quadratic optimization
Abstract
Let be the set of all the integer points in the transportation polytope of matrices with row sums and column sums . In this paper we find the sharp lower bound on the tropical determinant over the set . 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
