A binary constraint satisfaction problem (BCSP) consists in determining an assignment of values to variables that is compatible with a set of constraints. The problem is called binary because the constraints involve only pairs of variables. The BCSP is a cornerstone problem in Constraint Programming (CP), appearing in a very wide range of real-world applications. In this work, we develop a new exact algorithm which effectively solves the BCSP by reformulating it as a $k$-clique problem on the underlying microstructure graph representation. Our new algorithm exploits the cutting-edge branching scheme of the state-of-the-art maximum clique algorithms combined with two filtering phases in which the domains of the variables are reduced. Our filtering phases are based on colouring techniques and on heuristically solving an associated boolean satisfiability (SAT) problem. In addition, the algorithm initialization phase performs a reordering of the microstructure graph vertices that produces an often easier reformulation to solve. We carry out an extensive computational campaign on a benchmark of almost 2000 instances, encompassing numerous real and synthetic problems from the literature. The performance of the new algorithm is compared against four SAT-based solvers and three general purpose CP solvers. Our tests reveal that the new algorithm significantly outperforms all the others in several classes of BCSP instances.

二元约束满足问题 (BCSP) 包括确定与一组约束兼容的变量的值分配。这个问题被称为二元问题，因为约束只涉及成对的变量。BCSP 是约束编程 (CP) 中的一个基石问题，出现在非常广泛的实际应用程序中。在这项工作中，我们开发了一种新的精确算法，通过将 BCSP 重新表述为$ķ$-关于底层微观结构图表示的集团问题。我们的新算法利用了最先进的最大团算法的尖端分支方案，并结合了两个过滤阶段，其中变量的域被减少。我们的过滤阶段基于着色技术和启发式解决相关的布尔可满足性 (SAT) 问题。此外，算法初始化阶段执行微观结构图顶点的重新排序，从而产生通常更容易解决的重新表述。我们在近 2000 个实例的基准上进行了广泛的计算活动，包括文献中的许多真实和综合问题。新算法的性能与四个基于 SAT 的求解器和三个通用 CP 求解器进行了比较。