### Abstract

In this paper we study a few important tree optimization problems with applications to computational biology. These problems ask for trees that are consistent with an as large part, of the given data as possible. We show that the maximum homeomorphic agreement subtree problem cannot be approximated within a factor of Nε, where N is the input size, for any 0 ≤ ε < 1/18 in polynomial time unless P=NP, even if all the given trees are of height 2. On the other hand, we present an O(N log N)-time heuristic for the restriction of this problem to instances with O(1) trees of height O(1) yielding solutions within a constant factor of the optimum. We prove that the maximum inferred consensus tree problem is NP-complete, and we provide a simple fast heuristic for it yielding solutions within one third of the optimum. We also present a more specialized polynomial-time heuristic for the maximum inferred local consensus tree problem.

Original language | English (US) |
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Title of host publication | Computing and Combinatorics - 3rd Annual International Conference COCOON 1997, Proceedings |

Editors | Tao Jiang, D.T. Lee |

Publisher | Springer Verlag |

Pages | 134-145 |

Number of pages | 12 |

ISBN (Print) | 354063357X, 9783540633570 |

DOIs | |

State | Published - 1997 |

Externally published | Yes |

Event | 3rd Annual International Computing and Combinatorics Conference, COCOON 1997 - Shanghai, China Duration: Aug 20 1997 → Aug 22 1997 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1276 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 3rd Annual International Computing and Combinatorics Conference, COCOON 1997 |
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Country | China |

City | Shanghai |

Period | 8/20/97 → 8/22/97 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Computing and Combinatorics - 3rd Annual International Conference COCOON 1997, Proceedings*(pp. 134-145). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1276). Springer Verlag. https://doi.org/10.1007/bfb0045080