AI 中文总结
针对枚举领域重要开放问题，证明高效算法MMCS不是输出多项式，分析其启发式选择对运行时间的影响，提出新扩展并通过实验验证其实际性能提升。
AI 中文摘要
横截超图问题是枚举给定超图$\u0398$的所有包含意义下的极小击中集，这是枚举领域最重要的开放问题，即该问题是否存在运行时间随$\u0398$的规模和解的数量呈多项式增长的输出多项式算法。目前，Murakami和Uno在《DAM 2014》中提出的极小到极大转换搜索（MMCS）是针对现实世界实例的最高效算法，但尚无其最坏情况性能保证。我们证明MMCS实际上不是输出多项式的，该下界构造促使更详细地分析算法设计中某些启发式选择对运行时间的影响。我们对这些启发式进行了全面分析，并在此基础上提出了新的扩展，随后通过大量运行时间实验表明，该新启发式进一步提升了实际性能。
英文摘要
The Transversal Hypergraph problem is to enumerate (list) all inclusion-wise minimal hitting sets of a given hypergraph $\mathcal{H}$. It is the most important open question in enumeration whether this problem admits an output-polynomial algorithm whose running time scales polynomially with the size of $\mathcal{H}$ and the number of solutions. Currently, Minimal-to-Maximal Conversion Search (MMCS) by Murakami and Uno [DAM 2014] is the most efficient algorithm for real-world instances, but there are no worst-case performance guarantees known for it. We prove that MMCS is in fact not output-polynomial. The lower bound construction motivates a more detailed analysis of how certain heuristic choices in the algorithm design affect the running time. We conduct a thorough analysis of those heuristics and, based on this, propose new extension. We then show in extensive running time experiments that this new heuristic further improves practical performance.
