On the frontiers of polynomial computations in tropical geometry
arXiv:math/0411012
Abstract
We study some basic algorithmic problems concerning the intersection of tropical hypersurfaces in general dimension: deciding whether this intersection is nonempty, whether it is a tropical variety, and whether it is connected, as well as counting the number of connected components. We characterize the borderline between tractable and hard computations by proving -hardness and #-hardness results under various strong restrictions of the input data, as well as providing polynomial time algorithms for various other restrictions.
17 pages, 5 figures. To appear in Journal of Symbolic Computation