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

2025-07-12

AI Summary

This paper addresses the complete enumeration of minimal hitting sets for a given family of sets—that is, finding all minimal subsets of elements that intersect every set in the family. We propose MinHit-ASP, the first systematic answer-set programming (ASP) formulation of this problem, enabling efficient, verifiable, and complete enumeration via off-the-shelf ASP solvers. Unlike conventional algorithms, MinHit-ASP supports uniform declarative modeling, automatic handling of complex constraints (e.g., cardinality bounds or element preferences), and exhibits strong scalability. Evaluated on diverse benchmarks from model-based diagnosis, bioinformatics, and formal verification, MinHit-ASP consistently outperforms state-of-the-art tools in both runtime and memory efficiency, while guaranteeing completeness. It thus establishes the first general-purpose, ASP-based framework for minimal hitting set enumeration.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Heuristic Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Enumerate minimal hitting sets efficiently
• Formulate problem using Answer Set Programming
• Develop ASP-based tool for diverse benchmarks

Innovation

• ASP-based tool for minimal hitting sets
• Leverages existing ASP solvers
• Effective across diverse benchmarks