### Abstract

The perfect phylogeny problem is a classical problem in computational evolutionary biology in which a set of species/taxa is described by a set of qualitative characters. In recent years, the problem has been shown to be NP-complete in general, while the different fixed parameter versions can each be solved in polynomial time. In particular, Agarwala and Fernández-Baca have developed an O(2^{3r}(nk^{3} + k^{4})) algorithm for the perfect phylogeny problem for n species defined by k r-state characters [SIAM J. Comput., 23 (1994), pp. 1216-1224]. Since, commonly, the character data are drawn from alignments of molecular sequences, k is the length of the sequences and can thus be very large (in the hundreds or thousands). Thus, it is imperative to develop algorithms which run efficiently for large values of k. In this paper we make additional observations about the structure of the problem and produce an algorithm for the problem that runs in time O(2^{2r}k^{2}n). We also show how it is possible to efficiently build a structure that implicitly represents the set of all perfect phytogenies and to randomly sample from that set.

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

Pages (from-to) | 1749-1763 |

Number of pages | 15 |

Journal | SIAM Journal on Computing |

Volume | 26 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Combinatorial enumeration
- Dynamic programming
- Evolutionary trees
- Perfect phylogeny
- Polynomial delay algorithms

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Theoretical Computer Science

### Cite this

*SIAM Journal on Computing*,

*26*(6), 1749-1763. https://doi.org/10.1137/S0097539794279067

**A fast algorithm for the computation and enumeration of perfect phylogenies.** / Kannan, Sampath; Warnow, Tandy.

Research output: Contribution to journal › Article

*SIAM Journal on Computing*, vol. 26, no. 6, pp. 1749-1763. https://doi.org/10.1137/S0097539794279067

}

TY - JOUR

T1 - A fast algorithm for the computation and enumeration of perfect phylogenies

AU - Kannan, Sampath

AU - Warnow, Tandy

PY - 1997/12

Y1 - 1997/12

N2 - The perfect phylogeny problem is a classical problem in computational evolutionary biology in which a set of species/taxa is described by a set of qualitative characters. In recent years, the problem has been shown to be NP-complete in general, while the different fixed parameter versions can each be solved in polynomial time. In particular, Agarwala and Fernández-Baca have developed an O(23r(nk3 + k4)) algorithm for the perfect phylogeny problem for n species defined by k r-state characters [SIAM J. Comput., 23 (1994), pp. 1216-1224]. Since, commonly, the character data are drawn from alignments of molecular sequences, k is the length of the sequences and can thus be very large (in the hundreds or thousands). Thus, it is imperative to develop algorithms which run efficiently for large values of k. In this paper we make additional observations about the structure of the problem and produce an algorithm for the problem that runs in time O(22rk2n). We also show how it is possible to efficiently build a structure that implicitly represents the set of all perfect phytogenies and to randomly sample from that set.

AB - The perfect phylogeny problem is a classical problem in computational evolutionary biology in which a set of species/taxa is described by a set of qualitative characters. In recent years, the problem has been shown to be NP-complete in general, while the different fixed parameter versions can each be solved in polynomial time. In particular, Agarwala and Fernández-Baca have developed an O(23r(nk3 + k4)) algorithm for the perfect phylogeny problem for n species defined by k r-state characters [SIAM J. Comput., 23 (1994), pp. 1216-1224]. Since, commonly, the character data are drawn from alignments of molecular sequences, k is the length of the sequences and can thus be very large (in the hundreds or thousands). Thus, it is imperative to develop algorithms which run efficiently for large values of k. In this paper we make additional observations about the structure of the problem and produce an algorithm for the problem that runs in time O(22rk2n). We also show how it is possible to efficiently build a structure that implicitly represents the set of all perfect phytogenies and to randomly sample from that set.

KW - Combinatorial enumeration

KW - Dynamic programming

KW - Evolutionary trees

KW - Perfect phylogeny

KW - Polynomial delay algorithms

UR - http://www.scopus.com/inward/record.url?scp=0008827068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0008827068&partnerID=8YFLogxK

U2 - 10.1137/S0097539794279067

DO - 10.1137/S0097539794279067

M3 - Article

AN - SCOPUS:0008827068

VL - 26

SP - 1749

EP - 1763

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 6

ER -