On the frontiers of polynomial computations in tropical geometry

• Autores: Thorsten Theobald
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 41, Nº 12, 2006, págs. 1360-1375
• Idioma: inglés
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• Resumen

  • 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.