We study the enumeration complexity of Unions of Conjunctive Queries (UCQs) . We aim to identify the UCQs that are tractable in the sense that the answer tuples can be enumerated with a linear preprocessing phase and a constant delay between every successive tuples. It has been established that, in the absence of self-joins and under conventional complexity assumptions, the CQs that admit such an evaluation are precisely the free-connex ones. A union of tractable CQs is always tractable. We generalize the notion of free-connexity from CQs to UCQs, thus showing that some unions containing intractable CQs are, in fact, tractable. Interestingly, some unions consisting of only intractable CQs are tractable too. We show how to use the techniques presented in this article also in settings where the database contains cardinality dependencies (including functional dependencies and key constraints) or when the UCQs contain disequalities. The question of finding a full characterization of the tractability of UCQs remains open. Nevertheless, we prove that, for several classes of queries, free-connexity fully captures the tractable UCQs.

中文翻译：

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论合取查询并集的枚举复杂度

我们研究枚举复杂度联合查询 (UCQ). 我们的目标是确定易于处理的 UCQ，因为答案元组可以通过线性预处理阶段和每个连续元组之间的恒定延迟来枚举。已经确定，在没有自连接和传统复杂性假设的情况下，接受这种评估的 CQ 恰好是自由连接的 CQ。易处理的 CQ 的联合总是易处理的。我们将自由连接的概念从 CQ 推广到 UCQ，从而表明一些包含棘手 CQ 的联合实际上是易于处理的。有趣的是，一些只由难以处理的 CQ 组成的工会也很容易处理。我们还将展示如何在数据库包含基数依赖（包括函数依赖和关键约束）或 UCQ 包含不等式的设置中使用本文中介绍的技术。找到 UCQ 可处理性的完整特征的问题仍然悬而未决。尽管如此，我们证明，对于几类查询，自由连接完全捕获了可处理的 UCQ。