The constraint satisfaction problem (CSP) has important applications in computer science and AI. In particular, infinite-domain CSPs have been intensively used in subareas of AI such as spatio-temporal reasoning. Since constraint satisfaction is a computationally hard problem, much work has been devoted to identifying restricted problems that are efficiently solvable. One way of doing this is to restrict the interactions of variables and constraints, and a highly successful approach is to bound the treewidth of the underlying primal graph. Bodirsky & Dalmau [J. Comput. System. Sci. 79(1), 2013] and Huang et al. [Artif. Intell. 195, 2013] proved that CSP$(\Gamma)$ can be solved in $n^{f(w)}$ time (where $n$ is the size of the instance, $w$ is the treewidth of the primal graph and $f$ is a computable function) for certain classes of constraint languages $\Gamma$. We improve this bound to $f(w) \cdot n^{O(1)}$, where the function $f$ only depends on the language $\Gamma$, for CSPs whose basic relations have the patchwork property. Hence, such problems are fixed-parameter tractable and our algorithm is asymptotically faster than the previous ones. Additionally, our approach is not restricted to binary constraints, so it is applicable to a strictly larger class of problems than that of Huang et al. However, there exist natural problems that are covered by Bodirsky & Dalmau's algorithm but not by ours, and we begin investigating ways of generalising our results to larger families of languages. We also analyse our algorithm with respect to its running time and show that it is optimal (under the Exponential Time Hypothesis) for certain languages such as Allen's Interval Algebra.

翻译：限制满意度问题( CSP) 在计算机科学和AI 中有着重要的应用。 特别是, 无穷的 CSP 被大量用于AI 的子领域, 如spatio- 时间推理 。 由于限制满意度是一个计算上很困难的问题, 许多工作都致力于找出高效溶解的限制性问题 。 这样做的方法之一是限制变量和限制的相互作用, 一个非常成功的方法是将基础原始图的树枝连接起来 。 Bodirsky & Dalmau [J. Comput. Sci. 79(1), 2013] 和 Huang 等人 的子领域, 如 spotrealif. Intell. 195, 2013] 。 事实证明 CSP$ (\ gamma) 美元可以用$( gamma) 时间( 其中美元是原始图形和 $( $) 美元) 的树枝和 $( 美元) 等限制语言的树枝节功能 。 我们的硬度比 $( gamma) 的硬值要更好, 我们的硬值( 美元) 也比 美元( 美元) 直数( 美元) 直数( c) 直径) 的硬值( 直值) 直系的硬值) 的硬值( 直) 直) 的硬值( 也显示我们的硬值) 的硬值) 。