Bit-Parallel Tree Pattern Matching Algorithms for Unordered Labeled Trees

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(LP ·n·l·d h W e) time and O(n · l ·d h W e) space, and another one runs in O((LP ·n+h ·2) ·dh·l W e) time and O((n+h ·2) ·dh·l W e) 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 LP , 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 LP ≤ h. Finally, we give an algorithm to extract all occurrences from pseud-occurrences in O(n · LP · l) time and O(n · LP · l) space.