Testing idealness in the filter oracle model

Ahmad Abdi; Gérard Cornuéjols; Bertrand Guenin; Levent Tunçel

Testing idealness in the filter oracle model

Combinatorics 2022-02-16 v1 Optimization and Control

Authors: Ahmad Abdi , Gérard Cornuéjols , Bertrand Guenin , Levent Tunçel

Abstract

A filter oracle for a clutter consists of a finite set $V$ along with an oracle which, given any set $X\subseteq V$ , decides in unit time whether or not $X$ contains a member of the clutter. Let $\mathfrak{A}_{2n}$ be an algorithm that, given any clutter $\mathcal{C}$ over $2n$ elements via a filter oracle, decides whether or not $\mathcal{C}$ is ideal. We prove that in the worst case, $\mathfrak{A}_{2n}$ must make at least $2^n$ calls to the filter oracle. Our proof uses the theory of cuboids.

Keywords

ultrafilter

Cite

@article{arxiv.2202.07299,
  title  = {Testing idealness in the filter oracle model},
  author = {Ahmad Abdi and Gérard Cornuéjols and Bertrand Guenin and Levent Tunçel},
  journal= {arXiv preprint arXiv:2202.07299},
  year   = {2022}
}

Testing idealness in the filter oracle model

Abstract

Keywords

Cite

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