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A Proof of the CSP Dichotomy Conjecture
Journal of the ACM ( IF 2.5 ) Pub Date : 2020-08-26 , DOI: 10.1145/3402029
Dmitriy Zhuk 1
Affiliation  

Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The standard way to parameterize interesting subclasses of the constraint satisfaction problem is via finite constraint languages. The main problem is to classify those subclasses that are solvable in polynomial time and those that are NP-complete. It was conjectured that if a constraint language has a weak near-unanimity polymorphism then the corresponding constraint satisfaction problem is tractable; otherwise, it is NP-complete. In the article, we present an algorithm that solves Constraint Satisfaction Problem in polynomial time for constraint languages having a weak near unanimity polymorphism, which proves the remaining part of the conjecture. 1

中文翻译:

CSP 二分法猜想的证明

许多自然组合问题可以表示为约束满足问题。这类问题通常是已知的 NP 完全问题,但对约束形式的某些限制可以确保易处理性。参数化约束满足问题的有趣子类的标准方法是通过有限约束语言。主要问题是对那些在多项式时间内可解的子类和那些NP完全的子类进行分类。据推测,如果约束语言具有弱的近一致多态性,则相应的约束满足问题是易于处理的;否则,它是NP完全的。在本文中,我们提出了一种算法,该算法可以在多项式时间内解决具有弱近一致多态性的约束语言的约束满足问题,1
更新日期:2020-08-26
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