High Quality Content by WIKIPEDIA articles! In mathematics, the vertex enumeration problem for a polyhedron, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem of determination of the object's vertices given some formal representation of the object. The computational complexity of the problem is a subject of research in computer science. A 1992 article by D. Avis and K. Fukuda presents an algorithm which finds the v vertices of a polyhedron defined by a nondegenerate system of n inequalities in d dimensions (or, dually, the v facets of the convex hull of n points in d dimensions, where each facet contains exactly d given points) in time O(ndv) and O(nd) space. The v vertices in a simple arrangement of n hyperplanes in d dimensions can be found in O(n2dv) time and O(nd) space complexity.

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