## Abstract

We study the problem of constructing phylogenetic trees for a given set of species. The problem is formulated as that of finding a minimum Steiner tree on n points over the Boolean hypercube of dimension d. It is known that an optimal tree can be found in linear time [1] if the given dataset has a perfect phylogeny, i.e. cost of the optimal phylogeny is exactly d. Moreover, if the data has a near-perfect phylogeny, i.e. the cost of the optimal Steiner tree is d + q, it is known [2] that an exact solution can be found in running time which is polynomial in the number of species and d, yet exponential in q. In this work, we give a polynomial-time algorithm (in both d and q) that finds a phylogenetic tree of cost d + O(q ^{2}). This provides the best guarantees known-namely, a (1 + o(1))-approximation-for the case log(d) ≪ q ≪ √d, broadening the range of settings for which near-optimal solutions can be efficiently found. We also discuss the motivation and reasoning for studying such additive approximations.

Original language | English |
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Title of host publication | Approximation, Randomization, and Combinatorial Optimization |

Subtitle of host publication | Algorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings |

Pages | 25-36 |

Number of pages | 12 |

DOIs | |

State | Published - 2012 |

Externally published | Yes |

Event | 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012 - Cambridge, MA, United States Duration: 15 Aug 2012 → 17 Aug 2012 |

### 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 | 7408 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012 |
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Country/Territory | United States |

City | Cambridge, MA |

Period | 15/08/12 → 17/08/12 |

### Bibliographical note

Funding Information:This work was supported in part by the National Science Foundation under grant CCF-1116892, by an NSF Graduate Fellowship, and by the MSR-CMU Center for Computational Thinking.