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Fax: +81-011-706-7680Faster Bit-Parallel Algorithms for Unordered Pseudo-Tree Matching and Tree Homeomorphism

By Yusaku Kaneta and Hiroki ArimuraYusaku Kaneta and Hiroki Arimura


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-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 + m log 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.

Year: 2010
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