A Linear-Space Top-Down Algorithm for Tree Inclusion Problem

• Published in: 2012 International Conference on Computer Science and Service System pp. 85 - 89
• Main Authors: Yangjun Chen, Yibin Chen
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.08.2012
• Subjects: Algorithm design and analysis; Computer science; Data structures; Heuristic algorithms; Pattern matching; tree embedding; tree inclusion; tree matching; Vegetation
• DOI: 10.1109/CSSS.2012.30
• ISBN: 9781467307215; 1467307211

We consider the following tree-matching problem: Given labeled, ordered trees P and T, can P be obtained from T by deleting nodes? Deleting a node v entails removing all edges incident to v and, if v has a parent u, replacing the edges from u to v by edges from u to the children of v. The best known algorithm for this problem needs O(|T|·|leaves(P)|) time and O(|leaves(P)|·min{D T , |leaves(T)|} + |T| + |P|) space, where leaves(T) (resp. leaves(P)) stands for the set of the leaves of T (resp. P), and D T (resp. D P ) for the height of T (resp. P). In this paper, we present an efficient algorithm that requires O(|T|.|leaves(P)|) time and O(|T| + |P|) space.