Computing the EHZ capacity is NP-hard
Symplectic Geometry
2024-12-06 v3 Computational Complexity
Combinatorics
Abstract
The Ekeland-Hofer-Zehnder capacity (EHZ capacity) is a fundamental symplectic invariant of convex bodies. We show that computing the EHZ capacity of polytopes is NP-hard. For this we reduce the feedback arc set problem in bipartite tournaments to computing the EHZ capacity of simplices.
Cite
@article{arxiv.2402.09914,
title = {Computing the EHZ capacity is NP-hard},
author = {Karla Leipold and Frank Vallentin},
journal= {arXiv preprint arXiv:2402.09914},
year = {2024}
}
Comments
(v3) 10 pages, minor changes, Lemma 4.1 simplified, accepted in Proc. AMS