Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Polynomial-Time Algorithms for the Ordered Maximum Agreement Subtree Problem

  • 77 Accesses

Abstract

For a set of rooted, unordered, distinctly leaf-labeled trees, the NP-hard maximum agreement subtree problem (MAST) asks for a tree contained (up to isomorphism or homeomorphism) in all of the input trees with as many labeled leaves as possible. We study the ordered variants of MAST where the trees are uniformly or non-uniformly ordered. We provide the first known polynomial-time algorithms for the uniformly and non-uniformly ordered homeomorphic variants as well as the uniformly and non-uniformly ordered isomorphic variants of MAST. Our algorithms run in time \(O(kn^3)\), \(O(n^3 \min \{kn,\, n+\log^{k-1}n\})\), \(O(kn^3)\), and \(O(n^3 \min \{kn,\, n+\log^{k-1}n\})\), respectively, where n is the number of leaf labels and k is the number of input trees.

This is a preview of subscription content, log in to check access.

Author information

Correspondence to Anders Dessmark or Jesper Jansson or Andrzej Lingas or Eva-Marta Lundell.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dessmark, A., Jansson, J., Lingas, A. et al. Polynomial-Time Algorithms for the Ordered Maximum Agreement Subtree Problem. Algorithmica 48, 233–248 (2007). https://doi.org/10.1007/s00453-007-0080-9

Download citation

Keywords

  • Mast
  • Mast Problem
  • Input Tree
  • Longe Common Subsequence
  • Unordered Tree