We investigate the enumeration of query results for an important subset of CQs with projections, namely star and path queries. The task is to design data structures and algorithms that allow for efficient enumeration with delay guarantees after a preprocessing phase. Our main contribution is a series of results based on the idea of interleaving precomputed output with further join processing to maintain delay guarantees, which maybe of independent interest. In particular, we design combinatorial algorithms that provide instance-specific delay guarantees in nearly linear preprocessing time. These algorithms improve upon the currently best known results. Further, we show how existing results can be improved upon by using fast matrix multiplication. We also present {new} results involving tradeoff between preprocessing time and delay guarantees for enumeration of path queries that contain projections. CQs with projection where the join attribute is projected away is equivalent to boolean matrix multiplication. Our results can therefore be also interpreted as sparse, output-sensitive matrix multiplication with delay guarantees.

中文翻译：

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带投影的联合查询的枚举算法

我们调查了带有投影的重要CQ子集的查询结果的枚举，即星形查询和路径查询。任务是设计数据结构和算法，以允许在预处理阶段之后进行有效的枚举并保证延迟。我们的主要贡献是基于将预先计算的输出与进一步的连接处理进行交织以保持延迟保证的想法而得出的一系列结果，这可能是独立的利益。特别是，我们设计了组合算法，可以在接近线性的预处理时间内提供特定于实例的延迟保证。这些算法改进了当前最著名的结果。此外，我们展示了如何通过使用快速矩阵乘法来改善现有结果。我们还提出了{new}结果，涉及在预处理时间和延迟保证之间进行权衡，以枚举包含投影的路径查询。连接属性被投影掉的带有投影的CQ等效于布尔矩阵乘法。因此，我们的结果也可以解释为稀疏的，输出敏感的具有乘法保证的矩阵乘法。