MSO Queries on Trees: Enumerating Answers under Updates Using Forest Algebras

We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential interest for data structures and algorithms for trees whose complex...

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Veröffentlicht in:Logical methods in computer science Jg. 21, Issue 4
Hauptverfasser: Kleest-Meißner, Sarah, Marasus, Jonas, Niewerth, Matthias
Format: Journal Article
Sprache:Englisch
Veröffentlicht: 01.01.2025
ISSN:1860-5974, 1860-5974
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Abstract We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential interest for data structures and algorithms for trees whose complexity depend on the depth of the tree (representation). We provide an exemplary application of the framework to the problem of efficiently enumerating answers to MSO-definable queries over trees which are subject to local updates. We exhibit an algorithm that uses an O(n) preprocessing phase and enumerates answers with O(log(n)) delay between them. When the tree is updated, the algorithm can avoid repeating expensive preprocessing and restart the enumeration phase within O(log(n)) time. Our algorithms and complexity results in the paper are presented in terms of node-selecting tree automata representing the MSO queries.
AbstractList We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential interest for data structures and algorithms for trees whose complexity depend on the depth of the tree (representation). We provide an exemplary application of the framework to the problem of efficiently enumerating answers to MSO-definable queries over trees which are subject to local updates. We exhibit an algorithm that uses an O(n) preprocessing phase and enumerates answers with O(log(n)) delay between them. When the tree is updated, the algorithm can avoid repeating expensive preprocessing and restart the enumeration phase within O(log(n)) time. Our algorithms and complexity results in the paper are presented in terms of node-selecting tree automata representing the MSO queries.
Author Niewerth, Matthias
Kleest-Meißner, Sarah
Marasus, Jonas
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Snippet We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such representations can be computed...
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Title MSO Queries on Trees: Enumerating Answers under Updates Using Forest Algebras
Volume 21, Issue 4
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