English

Enumerating all minimal hitting sets in polynomial total time

Combinatorics 2024-12-06 v2 Data Structures and Algorithms

Abstract

Consider a hypergraph (=set system) H\mathbb{H} whose hh hyperedges are subsets of a set with w elements. We show that the RR minimal hitting sets of H\mathbb{H} can be enumerated in polynomial total time O(Rh2w2)O(Rh^2 w^2).

Cite

@article{arxiv.2303.07708,
  title  = {Enumerating all minimal hitting sets in polynomial total time},
  author = {Marcel Wild},
  journal= {arXiv preprint arXiv:2303.07708},
  year   = {2024}
}

Comments

There is a mistake in Case 1 of claim (4), which annihilates the proof of polynomial total time. This was pointed out independently by Arnaud Mary, then Endre Boros, then Martin Schirnek. My apologies for waiting so long with the withdrawal

R2 v1 2026-06-28T09:15:47.707Z