Many computational problems arising in, for instance, artificial intelligence can be realized as infinite-domain constraint satisfaction problems (CSPs) based on partition schemes: a set of pairwise disjoint binary relations (containing the equality relation) whose union spans the underlying domain and which is closed under converse. We first consider partition schemes that contain an acyclic order and where the constraint language contains all unions of the basic relations; such CSPs are frequently occurring in e.g. temporal and spatial reasoning. We identify properties of such orders which, when combined, are sufficient to establish NP-hardness of the CSP and strong lower bounds under the exponential-time hypothesis, even for degree-bounded problems. This result explains, in a uniform way, many existing hardness results from the literature, and shows that it is impossible to obtain subexponential time algorithms unless the exponential-time hypothesis fails. However, some of these problems (including several important temporal problems), despite likely not being solvable in subexponential time, admit non-trivial improved exponential-time algorithm, and we present a novel improved algorithm for RCC-8 and related formalisms.

例如，人工智能中出现的许多计算问题都可以实现为基于分区方案的无限域约束满足问题（CSP）：一组成对的不相交的二元关系（包含相等关系），其并集跨越基础域，并且在相反的情况下是封闭的。我们首先考虑包含非循环顺序的分区方案，其中约束语言包含基本关系的所有并集。这样的CSP经常在例如时间和空间推理中发生。我们确定了这些阶的性质，这些性质结合起来足以建立CSP的NP硬度和指数时间假设下的强下界，即使对于度界问题也是如此。该结果以统一的方式解释了文献中许多现有的硬度结果，并且表明除非指数时间假设失败，否则不可能获得次指数时间算法。然而，