The [[computational complexity]] of the problem is a subject of research in [[computer science]].
A 1992 article by D.[[David Avis]] and K.Komei Fukuda<ref>[http://www.springerlink.com/content/m7440v7p3440757u/ David Avis and Komei Fukuda, "A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra"], ''[[Discrete and Computational Geometry]]'', Volume 8, Number 1 / December, 1992, 295-313, {{doi|10.1007/BF02293050}}</ref> 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'' [[facet]]s of the [[convex hull]] of ''n'' points in ''d'' dimensions, where each facet contains exactly ''d'' given points) in time [[Big Oh notation|O]](''ndv'') and O(''nd'') [[space complexity|space]]. The ''v'' vertices in a simple arrangement of ''n'' [[hyperplane]]s in ''d'' dimensions can be found in O(''n''<sup>2</sup>''dv'') time and O(''nd'') space complexity. The Avis–Fukuda algorithm was related toadapted the [[criss-cross algorithm]] for oriented matroids.
