Convex Hulls, Oracles, and Homology
Metric Geometry
2007-05-23 v1 Combinatorics
Abstract
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).
Cite
@article{arxiv.math/0301100,
title = {Convex Hulls, Oracles, and Homology},
author = {Michael Joswig and G"unter M. Ziegler},
journal= {arXiv preprint arXiv:math/0301100},
year = {2007}
}
Comments
11 pages, 2 figures