### Abstract

Inferring the consensus of a set of different evolutionary trees for a given species set is a well-studied problem, for which several different models have been proposed. In this paper, we propose a new optimization problem for consensus tree construction, which we call the asymmetric median tree, (AMT). Our main theoretical result is the equivalence between the asymmetric median tree problem on k trees and the maximum independent set (MIS) problem on k-colored graphs. Although the problem is NP-hard for three or more trees, we have polynomial-time algorithms to construct the AMT for two trees and an approximation algorithm for three or more trees. We define a measure of phylogenetic resolution and show that our algorithms (both exact and approximate) produce consensus trees that on every input are at least as resolved as the standard models in use (strict consensus, majority tree, Nelson tree). Finally, we show that the AMT combines desirable features of many of the standard consensus tree models in use.

Original language | English (US) |
---|---|

Pages (from-to) | 311-335 |

Number of pages | 25 |

Journal | Discrete Applied Mathematics |

Volume | 71 |

Issue number | 1-3 |

DOIs | |

State | Published - Dec 5 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*,

*71*(1-3), 311-335. https://doi.org/10.1016/S0166-218X(96)00071-6

**The asymmetric median tree - A new model for building consensus trees.** / Phillips, Cynthia; Warnow, Tandy.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 71, no. 1-3, pp. 311-335. https://doi.org/10.1016/S0166-218X(96)00071-6

}

TY - JOUR

T1 - The asymmetric median tree - A new model for building consensus trees

AU - Phillips, Cynthia

AU - Warnow, Tandy

PY - 1996/12/5

Y1 - 1996/12/5

N2 - Inferring the consensus of a set of different evolutionary trees for a given species set is a well-studied problem, for which several different models have been proposed. In this paper, we propose a new optimization problem for consensus tree construction, which we call the asymmetric median tree, (AMT). Our main theoretical result is the equivalence between the asymmetric median tree problem on k trees and the maximum independent set (MIS) problem on k-colored graphs. Although the problem is NP-hard for three or more trees, we have polynomial-time algorithms to construct the AMT for two trees and an approximation algorithm for three or more trees. We define a measure of phylogenetic resolution and show that our algorithms (both exact and approximate) produce consensus trees that on every input are at least as resolved as the standard models in use (strict consensus, majority tree, Nelson tree). Finally, we show that the AMT combines desirable features of many of the standard consensus tree models in use.

AB - Inferring the consensus of a set of different evolutionary trees for a given species set is a well-studied problem, for which several different models have been proposed. In this paper, we propose a new optimization problem for consensus tree construction, which we call the asymmetric median tree, (AMT). Our main theoretical result is the equivalence between the asymmetric median tree problem on k trees and the maximum independent set (MIS) problem on k-colored graphs. Although the problem is NP-hard for three or more trees, we have polynomial-time algorithms to construct the AMT for two trees and an approximation algorithm for three or more trees. We define a measure of phylogenetic resolution and show that our algorithms (both exact and approximate) produce consensus trees that on every input are at least as resolved as the standard models in use (strict consensus, majority tree, Nelson tree). Finally, we show that the AMT combines desirable features of many of the standard consensus tree models in use.

UR - http://www.scopus.com/inward/record.url?scp=0042014724&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042014724&partnerID=8YFLogxK

U2 - 10.1016/S0166-218X(96)00071-6

DO - 10.1016/S0166-218X(96)00071-6

M3 - Article

AN - SCOPUS:0042014724

VL - 71

SP - 311

EP - 335

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 1-3

ER -