On the frontiers of polynomial computations in tropical geometry
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 NP-hardness and #P-hardness results under various strong restrictions of the input data, as well as providing polynomial time algorithms for various other restrictions. (c) 2006 Elsevier Ltd. All rights reserved.
tropical geometry tropical varieties np-hard polynomial time algorithms tropical prevarieties computational complexity