Faster Bit-Parallel Algorithms for Unordered Pseudo-tree Matching and Tree Homeomorphism

  • Yusaku Kaneta
  • Hiroki Arimura
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)


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-one embeddings that preserve node labels and parent-child relationship. This problem is closely related to tree pattern matching problem for XPath queries with child axis only. If m > w , we present an efficient algorithm that solves the problem in \(O(nm\ log(w)/w)\) time using O(hm/w + mlog(w)/w) space and O(m log(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. We also discuss a modification of our algorithm for the unordered tree homeomorphism problem, which corresponds to a tree pattern matching problem for XPath queries with descendant axis only.


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yusaku Kaneta
    • 1
  • Hiroki Arimura
    • 1
  1. 1.Hokkaido UniversitySapporoJapan

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