TY - JOUR

T1 - Approximate labelled subtree homeomorphism

AU - Pinter, Ron Y.

AU - Rokhlenko, Oleg

AU - Tsur, Dekel

AU - Ziv-Ukelson, Michal

PY - 2008/9/1

Y1 - 2008/9/1

N2 - 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 (m2 n / log m + m n 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 (m n) algorithm for rooted ordered trees and O (m n log m) and O (m n) algorithms for unrooted cyclically ordered and unrooted linearly ordered trees, respectively.

AB - 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 (m2 n / log m + m n 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 (m n) algorithm for rooted ordered trees and O (m n log m) and O (m n) algorithms for unrooted cyclically ordered and unrooted linearly ordered trees, respectively.

KW - Approximate labelled matching

KW - Tree similarity

UR - http://www.scopus.com/inward/record.url?scp=47549115072&partnerID=8YFLogxK

U2 - 10.1016/j.jda.2007.07.001

DO - 10.1016/j.jda.2007.07.001

M3 - Article

AN - SCOPUS:47549115072

VL - 6

SP - 480

EP - 496

JO - Journal of Discrete Algorithms

JF - Journal of Discrete Algorithms

SN - 1570-8667

IS - 3

ER -