### Abstract

The problem of constructing trees given a matrix of interleaf distances is motivated by applications in computational evolutionary biology and linguistics. The general problem is to find an edge-weighted tree which most closely approximates (under some norm) the distance matrix. Although the construction problem is easy when the tree exactly fits the distance matrix, optimization problems under all popular criteria are either known or conjectured to be NP-complete. In this paper we consider the related problem where we are given a partial order on the pairwise distances, and wish to construct (if possible) an edge-weighted tree realizing the partial order. In particular we are interested in partial orders which arise from experiments on triples of species. We will show that the consistency problem is NP-hard in general, but that for certain special cases the construction problem can be solved in polynomial time.

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings |

Editors | Frank Dehne, Jorg-Rudiger Sack, Nicola Santoro, Sue Whitesides |

Publisher | Springer-Verlag |

Pages | 397-408 |

Number of pages | 12 |

ISBN (Print) | 9783540571551 |

State | Published - Jan 1 1993 |

Externally published | Yes |

Event | 3rd Workshop on Algorithms and Data Structures, WADS 1993 - Montreal, Canada Duration: Aug 11 1993 → Aug 13 1993 |

### 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 | 709 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd Workshop on Algorithms and Data Structures, WADS 1993 |
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Country | Canada |

City | Montreal |

Period | 8/11/93 → 8/13/93 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings*(pp. 397-408). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 709 LNCS). Springer-Verlag.

**Tree reconstruction from partial orders.** / Kannan, Sampath; Warnow, Tandy.

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

*Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 709 LNCS, Springer-Verlag, pp. 397-408, 3rd Workshop on Algorithms and Data Structures, WADS 1993, Montreal, Canada, 8/11/93.

}

TY - GEN

T1 - Tree reconstruction from partial orders

AU - Kannan, Sampath

AU - Warnow, Tandy

PY - 1993/1/1

Y1 - 1993/1/1

N2 - The problem of constructing trees given a matrix of interleaf distances is motivated by applications in computational evolutionary biology and linguistics. The general problem is to find an edge-weighted tree which most closely approximates (under some norm) the distance matrix. Although the construction problem is easy when the tree exactly fits the distance matrix, optimization problems under all popular criteria are either known or conjectured to be NP-complete. In this paper we consider the related problem where we are given a partial order on the pairwise distances, and wish to construct (if possible) an edge-weighted tree realizing the partial order. In particular we are interested in partial orders which arise from experiments on triples of species. We will show that the consistency problem is NP-hard in general, but that for certain special cases the construction problem can be solved in polynomial time.

AB - The problem of constructing trees given a matrix of interleaf distances is motivated by applications in computational evolutionary biology and linguistics. The general problem is to find an edge-weighted tree which most closely approximates (under some norm) the distance matrix. Although the construction problem is easy when the tree exactly fits the distance matrix, optimization problems under all popular criteria are either known or conjectured to be NP-complete. In this paper we consider the related problem where we are given a partial order on the pairwise distances, and wish to construct (if possible) an edge-weighted tree realizing the partial order. In particular we are interested in partial orders which arise from experiments on triples of species. We will show that the consistency problem is NP-hard in general, but that for certain special cases the construction problem can be solved in polynomial time.

UR - http://www.scopus.com/inward/record.url?scp=85029502449&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029502449&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85029502449

SN - 9783540571551

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

SP - 397

EP - 408

BT - Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings

A2 - Dehne, Frank

A2 - Sack, Jorg-Rudiger

A2 - Santoro, Nicola

A2 - Whitesides, Sue

PB - Springer-Verlag

ER -