Approximate labelled subtree homeomorphism

Authors:
Ron Y. Pinter;Oleg Rokhlenko;Dekel Tsur;Michal Ziv-Ukelson
Affiliations:
Department of Computer Science, Technion-Israel Institute of Technology, Haifa 32000, Israel;Department of Computer Science, Technion-Israel Institute of Technology, Haifa 32000, Israel;Department of Computer Science, Ben Gurion University of the Negev, Beer-Sheva 84105, Israel;Department of Computer Science, Ben Gurion University of the Negev, Beer-Sheva 84105, Israel
Venue:
Journal of Discrete Algorithms
Year:
2008

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Abstract

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(m^2n/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) algorithm for rooted ordered trees and O(mnlogm) and O(mn) algorithms for unrooted cyclically ordered and unrooted linearly ordered trees, respectively.