Faster bit-parallel algorithms for unordered pseudo-tree matching and tree homeomorphism

In this paper, we consider the unordered pseudo-tree matching problem, which is a problem of, given two unordered labeled trees P and T, finding all occurrences of P in T via such many-to-one matchings that preserve node labels and parent–child relationship. This problem is closely related to the tr...

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Bibliographic Details
Published in:Journal of discrete algorithms (Amsterdam, Netherlands) Vol. 14; pp. 119 - 135
Main Authors: Kaneta, Yusaku, Arimura, Hiroki, Raman, Rajeev
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2012
Subjects:
Bit-parallel algorithms
String matching
Tree matching
Unordered trees
XML queries
Tree matching
XML queries
Bit-parallel algorithms
Unordered trees
String matching
ISSN:1570-8667, 1570-8675
Online Access:Get full text
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Summary:In this paper, we consider the unordered pseudo-tree matching problem, which is a problem of, given two unordered labeled trees P and T, finding all occurrences of P in T via such many-to-one matchings that preserve node labels and parent–child relationship. This problem is closely related to the tree pattern matching problem for XPath queries with child axis only. If m>w, we present an efficient algorithm that solves the problem in O(nmlog(w)/w) time using O(hm/w+mlog(w)/w) space and O(mlog(w)) preprocessing on a unit-cost arithmetic RAM model with addition, where m is the number of nodes in P, n is the number of nodes in T, h is the height of T, and w is the word length, and we assume that w⩾logn. We also discuss a modification of our algorithm for the unordered tree homeomorphism problem, which corresponds to the tree pattern matching problem for XPath queries with descendant axis only.
ISSN:1570-8667
1570-8675
DOI:10.1016/j.jda.2011.12.018