Tropical Halfspaces
Combinatorics
2007-05-23 v3 Metric Geometry
Abstract
As a new concept tropical halfspaces are introduced to the (linear algebraic) geometry of the tropical semiring (R,min,+). This yields exterior descriptions of the tropical polytopes that were recently studied by Develin and Sturmfels in a variety of contexts. The key tool to the understanding is a newly defined sign of the tropical determinant, which shares remarkably many properties with the ordinary sign of the determinant of a matrix. The methods are used to obtain an optimal tropical convex hull algorithm in two dimensions.
Keywords
Cite
@article{arxiv.math/0312068,
title = {Tropical Halfspaces},
author = {Michael Joswig},
journal= {arXiv preprint arXiv:math/0312068},
year = {2007}
}
Comments
18 pages, 4 figures; v3: many new references, several minor changes, new layout, renumbering of the results