On the frontiers of polynomial computations in tropical geometry

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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 $\mathcal{NP}$-hardness and #$\mathcal{P}$-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

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Combinatorics, 52B70; 68W30

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http://salesiana.dossiersoluciones.com/handle/123456789/100924

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0411012
 http://arxiv.org/abs/math/0411012

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arXiv