A Simple and Effective ASP-Based Tool for Enumerating Minimal Hitting Sets

TL;DR

This paper introduces MinHit-ASP, an ASP-based tool that efficiently enumerates all minimal hitting sets for a family of sets, demonstrating effectiveness across diverse benchmarks.

Contribution

The paper presents a novel ASP formulation and tool for complete enumeration of minimal hitting sets, leveraging ASP solvers for improved efficiency.

Findings

Effective enumeration across multiple benchmarks

Outperforms existing methods in efficiency

Demonstrates versatility across problem domains

Abstract

The hitting set problem is a fundamental problem in computer science and mathematics. Given a family of sets over a universe of elements, a minimal hitting set is a subset-minimal collection of elements that intersects each set in the family. Enumerating all minimal hitting sets is crucial in various real-world applications. In this paper, we address the full enumeration of all minimal hitting sets for a given family of sets. We formulate the problem using Answer Set Programming (ASP) and leverage existing ASP solvers for efficient enumeration. We propose an ASP-based tool, MinHit-ASP, and our empirical evaluation shows that it effectively enumerates minimal hitting sets across benchmarks from diverse problem domains.