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

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>wm>w, we present an efficient algorithm that solves the problem in O(nmlog(w)/w)O(nmlog(w)/w) time using O(hm/w+mlog(w)/w)O(hm/w+mlog(w)/w) space and O(mlog(w))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.