English

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

R2 v1 2026-06-28T14:49:32.852Z