Related papers: Abstract tropical linear programming
We consider a project that consists of a set of activities performed in parallel under constraints on their start and finish times, including start-finish precedence relationships, release start times, release end times, and deadlines. The…
We study a notion of tropical linear series on metric graphs that combines two essential properties of tropicalizations of linear series on algebraic curves: the Baker-Norine rank and the independence rank. Our main results relate the local…
One-sided linear systems of the form ``$Ax=b$'' are well-known and extensively studied over the tropical (max-plus) semiring and wide classes of related idempotent semirings. The usual approach is to first find the greatest solution to such…
Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral…
We introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality. The planar case is elementary, but a higher-dimensional generalization leads to an…
We define tropical analogues of the notions of linear space and Plucker coordinate and study their combinatorics. We introduce tropical analogues of intersection and dualization and define a tropical linear space built by repeated…
In this paper we further develop the theory of geometric tropicalization due to Hacking, Keel and Tevelev and we describe tropical methods for implicitization of surfaces. More precisely, we enrich this theory with a combinatorial formula…
In contrast to the situation in classical linear algebra, not every tropically non-singular matrix can be factored into a product of tropical elementary matrices. We do prove the factorizability of any tropically non-singular 2x2 matrix…
This paper proposes a tropical geometry-based edge detection framework that reformulates convolution and gradient computations using min-plus and max-plus algebra. The tropical formulation emphasizes dominant intensity variations,…
We show that, by using multiplicative weights in a game-theoretic thought experiment (and an important convexity result on the composition of multiplicative weights with the relative entropy function), a symmetric bimatrix game (that is, a…
Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus semiring arithmetic and matrix algebra. In this chapter we summarize some of their main ideas and common (geometric and algebraic) structure, generalize and…
Polyhedral projection is a main operation of the polyhedron abstract domain.It can be computed via parametric linear programming (PLP), which is more efficient than the classic Fourier-Motzkin elimination method.In prior work, PLP was done…
We apply an approach based on parametric mean-payoff games to develop bisection and Newton schemes for solving problems of tropical pseudolinear and pseudoquadratic optimisation with general two-sided constraints.
In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study…
Tropical differential equations are introduced and an algorithm is designed which tests solvability of a system of tropical linear differential equations within the complexity polynomial in the size of the system and in its coefficients.…
We develop a novel framework to construct and analyze finite valued, multidimensional mechanisms using tropical convex geometry. We geometrically characterize incentive compatibility using cells in the tropical convex hull of the type set.…
We present an algorithm for computing zero-dimensional tropical varieties using projections. Our main tools are fast unimodular transforms of lexicographical Gr\"obner bases. We prove that our algorithm requires only a polynomial number of…
We apply methods of tropical optimization to handle problems of rating alternatives on the basis of the log-Chebyshev approximation of pairwise comparison matrices. We derive a direct solution in a closed form, and investigate the obtained…
Tropical implicitization means computing the tropicalization of a unirational variety from its parametrization. In the case of a hypersurface, this amounts to finding the Newton polytope of the implicit equation, without computing its…
We consider decision problems of rating alternatives based on their pairwise comparisons according to two criteria. Given pairwise comparison matrices for each criterion, the problem is to find the overall scores of the alternatives. We…