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.

翻译：命中集问题是计算机科学与数学中的一个基础问题。给定元素全域上的集合族，最小命中集是与族中每个集合相交的元素子集极小集。枚举所有最小命中集在众多实际应用中至关重要。本文针对给定集合族的所有最小命中集进行完全枚举研究。我们采用答案集编程（ASP）对问题进行形式化建模，并利用现有ASP求解器实现高效枚举。我们提出了一种基于ASP的工具MinHit-ASP，实证评估表明该工具能有效枚举来自不同问题领域基准测试中的最小命中集。