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

  • Authors:

  • Yusaku Kaneta;Hiroki Arimura;Rajeev Raman

  • Affiliations:

  • Graduate School of Information Science and Technology, Hokkaido University, N14, W9, Sapporo 060-0814, Japan;Graduate School of Information Science and Technology, Hokkaido University, N14, W9, Sapporo 060-0814, Japan;Department of Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom

  • Venue:
  • Journal of Discrete Algorithms
  • Year:
  • 2012

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Abstract

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 mw, 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.