In this paper, we investigate the hitting set problem and demonstrate that solution independence is the crucial property underlying the construction of self-referential instances. As a special case of the hitting set problem, the vertex cover problem lacks the solution independence property. This distinction accounts for its ability to evade exhaustive search, as correlations among candidate solutions can be leveraged to compress the overall search space. In contrast, the dominating set problem on hypergraphs, which is also a special case of the hitting set problem, satisfies the solution independence property, thereby enabling the construction of self-referential instances. Moreover, we prove that these self-referential instances possess an irreducible property, implying that any algorithm for solving such instances must process nearly the entire graph to yield a correct solution.

翻译：本文研究了击中集问题，并证明了解独立性是构造自指实例的关键性质。作为击中集问题的特例，顶点覆盖问题不具备解独立性。这一差异解释了其能够避免穷举搜索的原因，即候选解之间的相关性可用于压缩整体搜索空间。相比之下，超图上的支配集问题（同样是击中集问题的特例）满足解独立性，从而能够构造自指实例。此外，我们证明了这些自指实例具有不可约性，这意味着任何求解此类实例的算法都必须处理几乎整个图才能得出正确解。