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- W2481446463 abstract "Over the last years the vertex enumeration problem of polyhedra has seen a revival in the study of metabolic networks, which increased the demand for efficient vertex enumeration algorithms for high-dimensional polyhedra given by inequalities. It is a famous and long standing open question in polyhedral theory and computational geometry whether the vertices of a polytope (bounded polyhedron), described by a set of linear constraints, can be enumerated in total polynomial time. In this paper we apply the concept of branch-decomposition to the vertex enumeration problem of polyhedra $P = {x : Ax = b, x geq 0}$. For this purpose, we introduce the concept of $k$-module and show how it relates to the separators of the linear matroid generated by the columns of $A$. We then use this to present a total polynomial time algorithm for polytopes $P$ for which the branch-width of the linear matroid generated by $A$ is bounded by a constant $k$." @default.
- W2481446463 created "2016-08-23" @default.
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- W2481446463 date "2014-04-22" @default.
- W2481446463 modified "2023-09-27" @default.
- W2481446463 title "Polynomial time vertex enumeration of convex polytopes of bounded branch-width" @default.
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