顽固问题不再顽固（3相容着色的多项式算法和顽固列表划分问题）
The stubborn problem is stubborn no more (a polynomial algorithm for 3-compatible colouring and the stubborn list partition problem)
摘要：
在CSP领域的驱动问题之一是二分法猜想，制定了在1993年由Feder和Vardi [STOC'93]，说明任何固定的关系结构G的约束满足问题CSP（G）是NP-完全或多项式时间可解。大量的研究已经进入检查各种具体情况下，这一猜想。其中一个变种，吸引了很多注意力，在最近几年是列表矩阵划分问题。在2004年，Cameron等人[SODA'04]对大小最多为4的矩阵的几乎所有LIST MATRIX PARTITION变体进行了分类。唯一一个抵制这种分类的案例被称为顽固问题。在本文中，我们展示了一个结果，使我们能够完成分类-从而解决了一个问题，抵御攻击的过去六年。我们的方法是基于一个组合的问题，已知至少是硬的顽固问题-3-相容的colorimetry问题。在这个问题中，我们给出了一个完全图，每个边都被分配了3种可能的颜色之一，我们希望将这3种颜色中的一种分配给每个顶点，使得没有边的颜色与它的两个端点相同。3-相容色问题的易处理性已经公开了好几年，在本文之前最著名的算法是Feder等人的[SODA'05] -一个具有n^O（log n / log log n）时间复杂度的拟多项式算法。在本文中，我们提出了一个多项式时间算法的3-相容色问题，从而我们证明了一个二分法的k-相容色问题。
英文摘要：
One of the driving problems in the CSP area is the Dichotomy Conjecture, formulated in 1993 by Feder and Vardi [STOC'93], stating that for any fixed relational structure G the Constraint Satisfaction Problem CSP(G) is either NP--complete or polynomial time solvable. A large amount of research has gone into checking various specific cases of this conjecture. One such variant which attracted a lot of attention in the recent years is the LIST MATRIX PARTITION problem. In 2004 Cameron et al. [SODA'04] classified almost all LIST MATRIX PARTITION variants for matrices of size at most four. The only case which resisted the classification became known as the STUBBORN PROBLEM. In this paper we show a result which enables us to finish the classification - thus solving a problem which resisted attacks for the last six years. Our approach is based on a combinatorial problem known to be at least as hard as the STUBBORN PROBLEM - the 3-COMPATIBLE COLOURING problem. In this problem we are given a complete graph with each edge assigned one of 3 possible colours and we want to assign one of those 3 colours to each vertex in such a way that no edge has the same colour as both of its endpoints. The tractability of the 3-COMPATIBLE COLOURING problem has been open for several years and the best known algorithm prior to this paper is due to Feder et al. [SODA'05] - a quasipolynomial algorithm with a n^O(log n / log log n) time complexity. In this paper we present a polynomial-time algorithm for the 3-COMPATIBLE COLOURING problem and consequently we prove a dichotomy for the k-COMPATIBLE COLOURING problem.
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。
