Computational Complexity
The computational complexity of the problem is a subject of research in computer science.
A 1992 article by David Avis and Komei Fukuda presents an algorithm which finds the v vertices of a polytope 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 space O(nd). 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. The Avis–Fukuda algorithm adapted the criss-cross algorithm for oriented matroids.
Read more about this topic: Vertex Enumeration Problem
Famous quotes containing the word complexity:
“The price we pay for the complexity of life is too high. When you think of all the effort you have to put in—telephonic, technological and relational—to alter even the slightest bit of behaviour in this strange world we call social life, you are left pining for the straightforwardness of primitive peoples and their physical work.”
—Jean Baudrillard (b. 1929)