Convex Hulls, Oracles, and Homology

Details Convex Hulls, Oracles, and Homology Convex Hulls, Oracles, and Homology

2003-01-10

arxiv.org/abs/math/0301100v1

Mathematics

Metric Geometry

11 pages, 2 figures

Scientific paper

This paper presents a new algorithm for the convex hull problem, which is based on a reduction to a combinatorial decision problem POLYTOPE-COMPLETENESS-COMBINATORIAL, which in turn can be solved by a simplicial homology computation. Like other convex hull algorithms, our algorithm is polynomial (in the size of input plus output) for simplicial or simple input. We show that the ``no''-case of POLYTOPE-COMPLETENESS-COMBINATORIAL has a certificate that can be checked in polynomial time (if integrity of the input is guaranteed).

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