柔性原子对称关系代数网络满意问题的复杂性
The Complexity of Network Satisfaction Problems for Symmetric Relation Algebras with a Flexible Atom
摘要：
Robin Hirsch在1996年提出了“真正的大复杂性问题”：对所有有限关系代数A的网络满意度问题的计算复杂性进行分类。我们提供了一个完整的分类的情况下，A是对称的，并有一个灵活的原子;在这种情况下，问题是NP完全或在P的分类任务可以减少到的情况下，A是整数。如果一个有限积分关系代数有一个柔性原子，则它有一个正规表示B。然后，我们可以研究的计算复杂性的网络满意度问题的A使用泛代数方法，通过分析的多态性B。我们还使用了一个拉姆齐型的结果Nešetziil和Rödl和复杂性二分的结果Bulatov保守的有限域约束满足问题。
英文摘要：
Robin Hirsch posed in 1996 the 'Really Big Complexity Problem': classify the computational complexity of the network satisfaction problem for all finite relation algebras A. We provide a complete classification for the case that A is symmetric and has a flexible atom; in this case, the problem is NP-complete or in P. The classification task can be reduced to the case where A is integral. If a finite integral relation algebra has a flexible atom, then it has a normal representation B. We can then study the computational complexity of the network satisfaction problem of A using the universal-algebraic approach, via an analysis of the polymorphisms of B. We also use a Ramsey-type result of Nešetřil and Rödl and a complexity dichotomy result of Bulatov for conservative finite-domain constraint satisfaction problems.
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