重标号下树的计数
Enumeration on Trees under Relabelings
摘要：
我们研究如何评估MSO查询树上的自由变量，枚举算法的框架内。以前的工作已经展示了如何用线性时间预处理和每个输出的大小的线性延迟来枚举答案，即，自由一阶变量的常数时滞我们扩展这一结果，以支持relabelings，一种受限的更新操作树，允许我们改变节点标签。我们的主要结果表明，我们可以枚举的答案MSO查询树与线性时间预处理和延迟线性，在每个答案，同时支持在对数时间节点重新标记。为了证明这一点，我们重新使用基于电路的枚举结构，从我们早期的工作，并开发技术来维护其索引下的节点重新标记。我们还展示了如何枚举下重新标记可以应用于评估实际的查询语言，如聚合，分组，和参数化查询。
英文摘要：
We study how to evaluate MSO queries with free variables on trees, within the framework of enumeration algorithms. Previous work has shown how to enumerate answers with linear-time preprocessing and delay linear in the size of each output, i.e., constant-delay for free first-order variables. We extend this result to support relabelings, a restricted kind of update operations on trees which allows us to change the node labels. Our main result shows that we can enumerate the answers of MSO queries on trees with linear-time preprocessing and delay linear in each answer, while supporting node relabelings in logarithmic time. To prove this, we reuse the circuit-based enumeration structure from our earlier work, and develop techniques to maintain its index under node relabelings. We also show how enumeration under relabelings can be applied to evaluate practical query languages, such as aggregate, group-by, and parameterized queries.
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