A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
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Virtually no additional storage is required beyond the input data.
The output list produced is free of duplicates.
The algorithm is extremely simple, requires no data structures, and handles all degenerate cases.
The running time is output sensitive for nondegenerate inputs.
The algorithm is easy to parallelize efficiently.
For example, the algorithm finds thev vertices of a polyhedron inRd defined by a nondegenerate system ofn inequalities (or, dually, thev facets of the convex hull ofn points inRd, where each facet contains exactlyd given points) in timeO(ndv) andO(nd) space. Thev vertices in a simple arrangement ofn hyperplanes inRd can be found inO(n2dv) time andO(nd) space complexity. The algorithm is based on inverting finite pivot algorithms for linear programming.
KeywordsConvex Hull Span Tree Convex Polyhedron Enumeration Tree Hyperplane Arrangement
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