Bit-Parallel Tree Pattern Matching Algorithms for Unordered Labeled Trees

Abstract

The following tree pattern matching problem is considered: Given two unordered labeled trees P and T, find all occurrences of P in T. Here P and T are called a pattern tree and a target tree, respectively. We first introduce a new problem called the pseudo-tree pattern matching problem. Then we show two efficient bit-parallel algorithms for the pseudo-tree pattern matching problem. One runs in $O(L_P\cdot n\cdot l\cdot \lceil \frac{h}{W}\rceil)$ time and $O(n\cdot l\cdot \lceil \frac{h}{W}\rceil)$ space, and another one runs in $O((L_P\cdot n+h\cdot 2^l)\cdot \lceil \frac{h\cdot l}{W}\rceil)$ time and $O((n+h\cdot 2^l)\cdot \lceil \frac{h\cdot l}{W}\rceil)$ space, where n is the number of nodes in T, h and l are the height of P and the number of leaves of P, respectively, and W is the length of a computer-word. The parameter L _P , called a recursive level of P, is defined to be the number of occurrences of the same label on a path from the root to a leaf. Hence we have L _P  ≤ h. Finally, we give an algorithm to extract all occurrences from pseud-occurrences in $O(n\cdot L_P\cdot l^{3/2})$ time and O(n·L _P ·l) space.

This research was supported by the Ministry of Education, Sports, Culture, Science and Technology, Grant-in-Aid for Scientific Research (C).