We study the limits of linear time evaluation of conjunctive queries under constraints expressed as tuple-generating dependencies (TGDs), across several modes of query evaluation: single-testing, all-testing, counting, lexicographic direct access, and enumeration. While full classifications seem far beyond reach, we propose an approach that, for some evaluation modes and classes of TGDs, makes it possible to lift known dichotomies from the unconstrained setting. In particular, our approach applies to all mentioned evaluation modes except enumeration, when the constraints fall into one of two classes: non-recursive sets of TGDs in which every TGD uses at most binary relation symbols in the head or has at most two frontier variables; and frontier-guarded full TGDs. We further provide a collection of examples showcasing the challenges that arise for enumeration and for less restrictive classes of TGDs.

翻译：摘要：我们研究了在元组生成依赖（TGD）约束下，合取查询在多种查询评估模式中的线性时间评估极限，这些模式包括：单次测试、全测试、计数、词典序直接访问和枚举。虽然完整的分类似乎遥不可及，但我们提出了一种方法，对于某些评估模式和TGD类别，该方法能够将无约束环境中的已知二分法推广到约束环境。具体而言，当约束属于以下两类之一时，我们的方法适用于除枚举之外的所有提及的评估模式：非递归TGD集合，其中每个TGD的头部最多使用二元关系符号或最多有两个边界变量；以及边界保护的全TGD。我们进一步提供了一系列示例，展示了在枚举和限制较少的TGD类别中出现的挑战。