The minimal hitting set generation problem: algorithms and computation

TL;DR

This paper surveys twenty algorithms for generating minimal hitting sets, compares their performance on various inputs, and provides implementations for easy testing across different domains.

Contribution

It offers a comprehensive review of algorithms for minimal hitting set generation, including performance analysis and accessible implementations.

Findings

Algorithms vary significantly in computational efficiency.

Generation-focused algorithms outperform recognition methods in practical scenarios.

Open-source implementations facilitate broader research and application.

Abstract

Finding inclusion-minimal "hitting sets" for a given collection of sets is a fundamental combinatorial problem with applications in domains as diverse as Boolean algebra, computational biology, and data mining. Much of the algorithmic literature focuses on the problem of *recognizing* the collection of minimal hitting sets; however, in many of the applications, it is more important to *generate* these hitting sets. We survey twenty algorithms from across a variety of domains, considering their history, classification, useful features, and computational performance on a variety of synthetic and real-world inputs. We also provide a suite of implementations of these algorithms with a ready-to-use, platform-agnostic interface based on Docker containers and the AlgoRun framework, so that interested computational scientists can easily perform similar tests with inputs from their own research areas on their own computers or through a convenient Web interface.