### Abstract

We address a combinatorialprobl em which arises in computationalph ylogenetics. In this problem we are given a set of unrooted (not necessarily binary) trees each leaf-labelled by the same set S, and we wish to remove a minimum number of leaves so that the resultant trees share a common refinement (i.e. they are “compatible”. If we assume the input trees are all binary, then this is simply the Maximum Agreement Subtree problem (MAST), for which much is already known. However, if the input trees need not be binary, then the problem is much more computationally intensive: it is NP-hard for just two trees, and solvable in polynomial time for any number k of trees when all trees have bounded degree. In this paper we present an O(k^{2}n^{2}) 4-approximation algorithm and an O(k^{2}n^{3}) 3-approximation algorithm for the general case of this problem.

Original language | English (US) |
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Title of host publication | Approximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings |

Editors | Stefano Leonardi, Klaus Jansen, Vijay Vazirani |

Publisher | Springer-Verlag |

Pages | 122-134 |

Number of pages | 13 |

ISBN (Print) | 3540441867, 9783540441861 |

State | Published - Jan 1 2002 |

Externally published | Yes |

Event | 5th International Workshop On Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002 - Rome, Italy Duration: Sep 17 2002 → Sep 21 2002 |

### 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 | 2462 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 5th International Workshop On Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002 |
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Country | Italy |

City | Rome |

Period | 9/17/02 → 9/21/02 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Approximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings*(pp. 122-134). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2462). Springer-Verlag.

**Approximating the complement of the maximum compatible subset of leaves of k trees.** / Ganapathy, Ganeshkumar; Warnow, Tandy.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Approximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2462, Springer-Verlag, pp. 122-134, 5th International Workshop On Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002, Rome, Italy, 9/17/02.

}

TY - GEN

T1 - Approximating the complement of the maximum compatible subset of leaves of k trees

AU - Ganapathy, Ganeshkumar

AU - Warnow, Tandy

PY - 2002/1/1

Y1 - 2002/1/1

N2 - We address a combinatorialprobl em which arises in computationalph ylogenetics. In this problem we are given a set of unrooted (not necessarily binary) trees each leaf-labelled by the same set S, and we wish to remove a minimum number of leaves so that the resultant trees share a common refinement (i.e. they are “compatible”. If we assume the input trees are all binary, then this is simply the Maximum Agreement Subtree problem (MAST), for which much is already known. However, if the input trees need not be binary, then the problem is much more computationally intensive: it is NP-hard for just two trees, and solvable in polynomial time for any number k of trees when all trees have bounded degree. In this paper we present an O(k2n2) 4-approximation algorithm and an O(k2n3) 3-approximation algorithm for the general case of this problem.

AB - We address a combinatorialprobl em which arises in computationalph ylogenetics. In this problem we are given a set of unrooted (not necessarily binary) trees each leaf-labelled by the same set S, and we wish to remove a minimum number of leaves so that the resultant trees share a common refinement (i.e. they are “compatible”. If we assume the input trees are all binary, then this is simply the Maximum Agreement Subtree problem (MAST), for which much is already known. However, if the input trees need not be binary, then the problem is much more computationally intensive: it is NP-hard for just two trees, and solvable in polynomial time for any number k of trees when all trees have bounded degree. In this paper we present an O(k2n2) 4-approximation algorithm and an O(k2n3) 3-approximation algorithm for the general case of this problem.

UR - http://www.scopus.com/inward/record.url?scp=84956979382&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956979382&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84956979382

SN - 3540441867

SN - 9783540441861

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 122

EP - 134

BT - Approximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings

A2 - Leonardi, Stefano

A2 - Jansen, Klaus

A2 - Vazirani, Vijay

PB - Springer-Verlag

ER -