Compression with wildcards: All exact, or all minimal hitting sets

TL;DR

This paper introduces a novel method for efficiently enumerating all minimal hitting sets of hypergraphs using wildcards, outperforming traditional methods especially when high compression is achieved.

Contribution

The paper presents a new compression technique for enumerating minimal hitting sets, improving upon previous BDD-based approaches and including novel applications like Rado's Theorem.

Findings

Traditional enumeration methods are less efficient with high compression.

The proposed method excels in enumerating all exact or minimal-cardinality hitting sets.

Numerical experiments demonstrate superior performance of the new approach.

Abstract

Our main objective is the COMPRESSED enumeration (based on wildcards) of all minimal hitting sets of general hypergraphs. To the author's best knowledge the only previous attempt towards compression, due to Toda, is based on BDD's and much different from our techniques. Numerical experiments show that traditional one-by-one enumeration schemes cannot compete against compressed enumeration when the degree of compression is high. Our method works particularly well in these two cases: Either compressing all e x a c t hitting sets, or all m i n i m u m - cardinality hitting sets. In many aspects this version is better structured than its predecessor, and also contains some new material (such as an application of Rado's Theorem).