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- W2043920735 abstract "Tropical polyhedra are known to be representable externally, as intersections of finitely many tropical half-spaces. However, unlike in the classical case, the extreme rays of their polar cones provide external representations containing in general superfluous half-spaces. In this paper, we prove that any tropical polyhedral cone in R^n (also known as tropical polytope in the literature) admits an essentially unique minimal external representation. The result is obtained by establishing a (partial) anti-exchange property of half-spaces. Moreover, we show that the apices of the half-spaces appearing in such non-redundant external representations are vertices of the cell complex associated with the polyhedral cone. We also establish a necessary condition for a vertex of this cell complex to be the apex of a non-redundant half-space. It is shown that this condition is sufficient for a dense class of polyhedral cones having generic extremities." @default.
- W2043920735 created "2016-06-24" @default.
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- W2043920735 date "2013-05-01" @default.
- W2043920735 modified "2023-10-16" @default.
- W2043920735 title "Minimal external representations of tropical polyhedra" @default.
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- W2043920735 doi "https://doi.org/10.1016/j.jcta.2013.01.011" @default.
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