Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
431122 | Journal of Discrete Algorithms | 2008 | 17 Pages |
Given two undirected trees T and P, the Subtree Homeomorphism Problem is to find whether T has a subtree t that can be transformed into P by removing entire subtrees, as well as repeatedly removing a degree-2 node and adding the edge joining its two neighbors. In this paper we extend the Subtree Homeomorphism Problem to a new optimization problem by enriching the subtree-comparison with node-to-node similarity scores. The new problem, called Approximate Labelled Subtree Homeomorphism (ALSH), is to compute the homeomorphic subtree of T which also maximizes the overall node-to-node resemblance. We describe an O(m2n/logm+mnlogn)O(m2n/logm+mnlogn) algorithm for solving ALSH on unordered, unrooted trees, where m and n are the number of vertices in P and T , respectively. We also give an O(mn)O(mn) algorithm for rooted ordered trees and O(mnlogm)O(mnlogm) and O(mn)O(mn) algorithms for unrooted cyclically ordered and unrooted linearly ordered trees, respectively.