### Abstract

We consider the problem of aligning sequences related by a given evolutionary tree: given a fixed tree with its leaves labeled with sequences, find ancestral sequences to label the internal nodes so as to minimize the total cost of all the edges in the tree. The cost of an edge is the edit distance between the sequences labeling its endpoints. In this paper, we consider the case when the given tree is a regular d-ary tree for some fixed d and provide a d+1/d-1-approximation algorithm for this problem that runs in time O(d(2kn)d+ n^{2}k^{2}d) where k is the number of leaves in the tree and n is the maximum length of any of the sequences labeling the leaves. We also consider a new bottleneck objective in labeling the internal nodes. In this version, we wish to find the labeling of the internal nodes that minimizes the maximum cost of any edge in the tree. For this problem we provide a simple 2δ + 1-approximation algorithm where 8 is the depth of the given undirected tree defined as the maximum over all internal nodes of the number of edges from the internal node to a closest leaf. For phylogenetic trees on n nodes that have no internal nodes of degree two, δ ≤ lg n.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 330-339 |

Number of pages | 10 |

Volume | 937 |

ISBN (Print) | 3540600442, 9783540600442 |

DOIs | |

State | Published - 1995 |

Externally published | Yes |

Event | 6th Annual Symposium on Combinatorial Pattern Matching, CPM 1995 - Espoo, Finland Duration: Jul 5 1995 → Jul 7 1995 |

### 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 | 937 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 6th Annual Symposium on Combinatorial Pattern Matching, CPM 1995 |
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Country | Finland |

City | Espoo |

Period | 7/5/95 → 7/7/95 |

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

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## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 937, pp. 330-339). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 937). Springer Verlag. https://doi.org/10.1007/3-540-60044-2_52