We study the question of when we can answer a Conjunctive Query (CQ) with an ordering over the answers by constructing a structure for direct (random) access to the sorted list of answers, without actually materializing this list, so that the construction time is linear (or quasilinear) in the size of the database. In the absence of answer ordering, such a construction has been devised for the task enumerating query answers of free-connex acyclic CQs, so that the access time is logarithmic. Moreover, it follows from past results that within the class of CQs without self-joins, being free-connex acyclic is necessary for the existence of such a construction (under conventional assumptions in fine-grained complexity). In this work, we embark on the challenge of identifying the answer orderings that allow for ranked direct access with the above complexity guarantees. We begin with the class of lexicographic orderings and give a decidable characterization of the class of feasible such orderings for every CQ without self-joins. We then continue to the more general case of orderings by the sum of attribute scores. As it turns out, in this case ranked direct access is feasible only in trivial cases. Hence, to better understand the computational challenge at hand, we consider the more modest task of providing access to only one single answer (i.e., finding the answer at a given position). We indeed achieve a quasilinear-time algorithm for a subset of the class of full CQs without self-joins, by adopting a solution of Frederickson and Johnson to the classic problem of selection over sorted matrices. We further prove that none of the other queries in this class admit such an algorithm.

中文翻译：

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可直接访问联合查询排名答案的可操作订单

我们研究的问题是，何时可以通过构造直接（随机）访问已排序答案的列表的结构而不实际实现此列表的结构来构造答案，从而使构造时间为数据库大小的线性（或准线性）。在没有答案排序的情况下，针对枚举自由连接的无环CQ的查询答案的任务设计了一种结构，因此访问时间是对数的。此外，从过去的结果得出的结论是，在没有自连接的CQ类别中，对于这种结构的存在（在细粒度复杂性的常规假设下），必须有自由连接的无环结构。在这项工作中 我们面临着挑战，即要确定能够以上述复杂性保证进行排名直接访问的答案顺序。我们从字典顺序的类别开始，并对每个没有自连接的CQ给出可行的此类顺序的类别的可确定的特征。然后，我们通过属性得分的总和继续进行更一般的排序情况。事实证明，在这种情况下，仅在平凡的情况下，排名直接访问才可行。因此，为了更好地理解手头的计算难题，我们考虑了更为适度的任务，即仅提供对单个答案的访问（即，在给定位置找到答案）。我们确实为没有自连接的完整CQ类的子集实现了准线性时间算法，通过采用Frederickson和Johnson的解决方案来解决排序矩阵的经典选择问题。我们进一步证明，此类中的其他查询均不接受这种算法。