枚举同态
Enumerating Homomorphisms
摘要：
关系结构的同态问题是表示约束满足问题和数据库理论中各种问题的抽象方法。同态问题的决策版本在文献中得到了很多关注;特别是，变量和约束的图论结构影响问题复杂性的方式得到了深入研究。在这里，我们从类似的角度研究了具有多项式延迟的所有解的枚举问题。事实证明，枚举问题的行为与决策版本非常不同。我们给出的证据表明，这是不可能的，可以得到类似的决定版本的表征结果。然而，我们展示了非平凡的情况下，枚举可以与多项式延迟。
英文摘要：
The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of attention in literature; in particular, the way the graph-theoretical structure of the variables and constraints influences the complexity of the problem is intensively studied. Here we study the problem of enumerating all the solutions with polynomial delay from a similar point of view. It turns out that the enumeration problem behaves very differently from the decision version. We give evidence that it is unlikely that a characterization result similar to the decision version can be obtained. Nevertheless, we show nontrivial cases where enumeration can be done with polynomial delay.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
