M-Representation of Polytopes
Combinatorics
2023-03-10 v1
Abstract
We introduce the M-representation of polytopes, which makes it possible to compute linear transformations, convex hulls, and Minkowski sums with linear complexity in the dimension of the polytopes. When the polytope is a convex hull of a zonotope and a polytope, the representation size can be smaller than any of the known representations (V-representation, H-representation, and Z-representation). We also provide a variant of the M-representation: The chain representation is more compact and we can directly use it to compute linear transformations and convex hulls -- for all other operations on the chain representation, one requires a conversion to the M-representation.
Keywords
Cite
@article{arxiv.2303.05173,
title = {M-Representation of Polytopes},
author = {Sebastian Sigl and Matthias Althoff},
journal= {arXiv preprint arXiv:2303.05173},
year = {2023}
}