双弧有向图与保守多态
Bi-Arc Digraphs and Conservative Polymorphisms
摘要：
在本文中，我们研究类双弧有向图，重要的是从两个看似无关的角度。一方面，它们是有向图，在约束满足问题的研究中承认某些感兴趣的多态性;另一方面，它们是区间图的一个非常广泛的推广。双弧有向图是一类允许保守半格多态的有向图。人们对理解允许特定类型多态性的结构，特别是它们的识别算法很感兴趣。(Such这些问题被称为元问题。）令人惊讶的是，双弧有向图类也描述了允许某些其他类型的保守多态性的有向图类。因此，解决双弧有向图的识别问题解决了几种类型的保守多态性的有向图的元问题。具有保守半格多态性的有向图识别问题的复杂性是一个开放问题，而对于某些更复杂的关系结构，它是NP完全的。我们补充我们的结果，提供了一个完整的二分法分类，一般的关系结构有多项式或NP-完全识别问题的存在保守的半格多态性。双弧有向图也是区间图类的推广;事实上，对于对称的和自反的有向图，它可以简化为区间图类。它比区间图广泛得多，包括区间图的其他推广，如共阈值容差图和调整区间有向图。然而，它仍然是区间图的合理扩展，在这个意义上，它保留了区间图的吸引力。我们的主要结果是一个禁止的障碍特征，和多项式识别，双弧有向图类。
英文摘要：
In this paper we study the class of bi-arc digraphs, important from two seemingly unrelated perspectives. On the one hand, they are precisely the digraphs that admit certain polymorphisms of interest in the study of constraint satisfaction problems; on the other hand, they are a very broad generalization of interval graphs. Bi-arc digraphs is the class of digraphs that admit conservative semilattice polymorphisms. There is much interest in understanding structures that admit particular types of polymorphisms, and especially in their recognition algorithms. (Such problems are referred to as metaproblems.) Surprisingly, the class of bi-arc digraphs also describes the class of digraphs that admit certain other kinds of conservative polymorphisms. Thus solving the recognition problem for bi-arc digraphs solves the metaproblem for digraphs for several types of conservative polymorphisms. The complexity of the recognition problem for digraphs with conservative semilattice polymorphisms was an open problem, while it was known to be NP-complete for certain more complex relational structures. We complement our result by providing a complete dichotomy classification of which general relational structures have polynomial or NP-complete recognition problems for the existence of conservative semilattice polymorphisms. Bi-arc digraphs also generalizes the class of interval graphs; in fact it reduces to the class of interval graphs for symmetric and reflexive digraphs. It is much broader than interval graphs and includes other generalizations of interval graphs such as co-threshold tolerance graphs and adjusted interval digraphs. Yet, it is still a reasonable extension of interval graphs, in the sense that it keeps much of the appeal of interval graphs. Our main result is a forbidden obstruction characterization of, and a polynomial recognition for, the class of bi-arc digraphs.
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