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

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. Ifm > 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. 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.