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. © 2011 Elsevier B.V.
Kaneta, Y., Arimura, H., & Raman, R. (2012). Faster bit-parallel algorithms for unordered pseudo-tree matching and tree homeomorphism. In Journal of Discrete Algorithms (Vol. 14, pp. 119–135). https://doi.org/10.1016/j.jda.2011.12.018