## 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^{2} 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.

Original language | English |
---|---|

Pages (from-to) | 480-496 |

Number of pages | 17 |

Journal | Journal of Discrete Algorithms |

Volume | 6 |

Issue number | 3 |

DOIs | |

State | Published - 1 Sep 2008 |

## Keywords

- Approximate labelled matching
- Tree similarity

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics