Polynomial-time algorithms for the ordered maximum agreement subtree problem

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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.

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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computer Science

Keywords

  • algorithm, maximum agreement subtree, ordered tree, evolutionary tree, time complexity
Original languageEnglish
Pages (from-to)233-248
JournalAlgorithmica
Volume48
Issue number3
Publication statusPublished - 2007
Publication categoryResearch
Peer-reviewedYes