Approximate Labelled Subtree Homeomorphism

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/ log m + mn log n) 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) algorithm for rooted ordered trees and O(mn log m) and O(mn) algorithms for unrooted cyclically ordered and unrooted linearly ordered trees, respectively.

• Type: Conference
• Year: 2004
• Where: CPM
• Authors: Ron Y. Pinter, Oleg Rokhlenko, Dekel Tsur, Michal Ziv-Ukelson
• Keywords: CPM 2004, Node-to-node Similarity Scores, Overall Node-to-node Resemblance, Subtree Homeomorphism Problem