MSO queries on trees: enumerating answers under updates

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2014-07-14 DOI:10.1145/2603088.2603137

Katja Losemann, W. Martens

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引用次数: 22

Abstract

We investigate efficient view maintenance for MSO-definable queries over trees or, more precisely, efficient enumeration of answers to MSO-definable queries over words and trees which are subject to local updates. For words we exhibit an algorithm that uses an O(n) preprocessing phase and enumerates answers with O(log n) delay between them. When the word is updated, the algorithm can avoid repeating expensive preprocessing and restart the enumeration phase within O(log n) time. For trees, our algorithm uses O(n) preprocessing time, enumerates answers with O(log2 n) delay, and can restart enumeration within O(log2 n) time after receiving an update to the tree. This significantly improves the cost of recomputing the answers of a query from scratch. Our algorithms and complexity results in the paper are presented in terms of node-selecting automata representing the MSO queries.

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树上的MSO查询:在更新下枚举答案

我们研究了树上mso可定义查询的有效视图维护，或者更准确地说，研究了基于本地更新的词和树上mso可定义查询的有效答案枚举。对于单词，我们展示了一种算法，该算法使用O(n)预处理阶段，并枚举它们之间O(log n)延迟的答案。当单词更新时，算法可以避免重复昂贵的预处理，在O(log n)时间内重新开始枚举阶段。对于树，我们的算法使用O(n)预处理时间，以O(log2 n)延迟枚举答案，并且在接收到树的更新后可以在O(log2 n)时间内重新开始枚举。这大大提高了从头开始重新计算查询答案的成本。本文用节点选择自动机来表示MSO查询，给出了我们的算法和复杂度结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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