A linear optimization oracle for zonotope computation
Combinatorics
2021-12-15 v1 Metric Geometry
Optimization and Control
Abstract
A class of counting problems ask for the number of regions of a central hyperplane arrangement. By duality, this is the same as counting the vertices of a zonotope. We give several efficient algorithms, based on a linear optimization oracle, that solve this and related enumeration problems. More precisely, our algorithms compute the vertices of a zonotope from the set of its generators and inversely, recover the generators of a zonotope from its vertices. A variation of the latter algorithm also allows to decide whether a polytope, given as its vertex set, is a zonotope and when it is not, to compute its greatest zonotopal summand.
Cite
@article{arxiv.1912.02439,
title = {A linear optimization oracle for zonotope computation},
author = {Antoine Deza and Lionel Pournin},
journal= {arXiv preprint arXiv:1912.02439},
year = {2021}
}
Comments
22 pages, 2 figures