## On the complexity of distance-based evolutionary tree reconstruction (2003)

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Venue: | In SODA: ACM-SIAM Symposium on Discrete Algorithms |

Citations: | 14 - 0 self |

### BibTeX

@INPROCEEDINGS{King03onthe,

author = {Valerie King and Li Zhang and Yunhong Zhou},

title = {On the complexity of distance-based evolutionary tree reconstruction},

booktitle = {In SODA: ACM-SIAM Symposium on Discrete Algorithms},

year = {2003},

pages = {444--453}

}

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### Abstract

y\Lambda

### Citations

100 | A few logs suffice to build (almost) all trees I, Random Structures and Algorithms - Erdős, Steel, et al. - 1999 |

83 | Diskcovering, a fast-converging method for phylogenetic tree reconstruction
- Huson, Nettles, et al.
- 1999
(Show Context)
Citation Context ...he bound to the so-called “edge-depth” rather than the diameter of the tree 2sand thus reduced the DNA length needed from exponential to polynomial in terms of the number of species. A series of work =-=[4,5,9,3,2]-=-reduced the running time to O(n 2 ) [3] from the early high degree polynomial bound. In DNA-based distance estimation, if the distance between the sequences grows too large, the distance measure becom... |

81 | A robust model for finding optimal evolutionary tree
- Farach-Colton, Kannan, et al.
- 1993
(Show Context)
Citation Context ... error, beginning in 1977 with [14]. Optimal algorithms can be found in [10], [8], and[1]. Numerous techiques and models have been proposed to do tree reconstruction when the data is not accurate. In =-=[7]-=-, Farach et al. consider the existence of tree metric that is sandwiched by two distance metrics. In [4, 5], Erdos et al. showed that if a distance metric is not “far” from a tree metric, it then uniq... |

56 | Recovering a tree from the leaf colourations it generates under a Markov model
- Steel
- 1994
(Show Context)
Citation Context ...the mutation matrix M(e). There are many ways to define M(e), from the simplest two character symmetric model (Cavender-Farris(CF) model, or two-state Neyman model [4, 12]) to the most general model (=-=[13, 2]-=-). In our paper, we only consider the CF model as there is no inherent difficulty to go from the simplest to the most general model if we define edge weights as in [2]. In the CF model, Σ={0, 1}, and ... |

46 | Efficient algorithms for inverting evolution
- Farach, Kannan
- 1999
(Show Context)
Citation Context ...oblem of reconstructing trees when the distance information only approximates those in the true tree. Such problems arise naturally in DNA-based distance estimation methods. The methods, pioneered by =-=[6, 4]-=- and others, model the evolution as a stochastic process and use the DNA sequences to derive a measurement on the mutation distance between species on the tree. One can then apply distance-based metho... |

39 |
Additive evolutionary trees
- Waterman, Smith, et al.
- 1977
(Show Context)
Citation Context ...l the methods using those oracles, respectively, the relation-based method (also known as the experiment-based method in [10] or the quartet method in the unrooted case) and the distance-based method =-=[14]-=- . We measure complexity of such algorithms by the number of queries made to the oracle. Distance-based oracles are at least as powerful as relation-based oracles as each relation query can be simulat... |

23 |
An Optimal Algorithm to Reconstruct Trees from Additive Distance Data
- Hein
- 1989
(Show Context)
Citation Context ...ed work Upper bounds: There has been extensive work on reconstruction of trees using relation and distance oracles with no error, beginning in 1977 with [14]. Optimal algorithms can be found in [10], =-=[8]-=-, and[1]. Numerous techiques and models have been proposed to do tree reconstruction when the data is not accurate. In [7], Farach et al. consider the existence of tree metric that is sandwiched by tw... |

21 | Fast recovery of evolutionary trees with thousands of nodes
- Csuros
- 2002
(Show Context)
Citation Context ...he bound to the so-called “edge-depth” rather than the diameter of the tree 2sand thus reduced the DNA length needed from exponential to polynomial in terms of the number of species. A series of work =-=[4,5,9,3,2]-=-reduced the running time to O(n 2 ) [3] from the early high degree polynomial bound. In DNA-based distance estimation, if the distance between the sequences grows too large, the distance measure becom... |

18 | Tutorial on phylogenetic tree estimation
- Kim, Warnow
- 1999
(Show Context)
Citation Context ... mutated independently according to the mutation matrix M(e). There are many ways to define M(e), from the simplest two character symmetric model (Cavender-Farris(CF) model, or two-state Neyman model =-=[4, 12]-=-) to the most general model ([13, 2]). In our paper, we only consider the CF model as there is no inherent difficulty to go from the simplest to the most general model if we define edge weights as in ... |

13 |
Determining the evolutionary tree
- Kannan, Lawler, et al.
- 1996
(Show Context)
Citation Context ...hat takes two species and returns the distance between them in the tree. We call the methods using those oracles, respectively, the relation-based method (also known as the experiment-based method in =-=[10]-=- or the quartet method in the unrooted case) and the distance-based method [14] . We measure complexity of such algorithms by the number of queries made to the oracle. Distance-based oracles are at le... |

8 | The complexity of constructing evolutionary trees using experiments
- Brodal, Fagerberg, et al.
- 2001
(Show Context)
Citation Context ...s by comparisons. On the other hand, the distance-based method needs only O(n) queries. While there have been tight bounds on the complexity of relation-based methods, for both binary or k-ary trees (=-=[10, 1]-=-), the bounds for distance-based methods are not tight. In this paper, we first show a tight Ω(kn log k n) lower bound on the number of queries of distance-based methods for k-ary trees with n leaves.... |

7 | Provably fast and accurate recovery of evolutionary trees through harmonic greedy triplets
- Csűrös, Kao
(Show Context)
Citation Context ...he bound to the so-called “edge-depth” rather than the diameter of the tree 2sand thus reduced the DNA length needed from exponential to polynomial in terms of the number of species. A series of work =-=[4,5,9,3,2]-=-reduced the running time to O(n 2 ) [3] from the early high degree polynomial bound. In DNA-based distance estimation, if the distance between the sequences grows too large, the distance measure becom... |

5 | Balanced randomized tree splitting with applications to evolutionary tree constructions
- Kao, Lingas, et al.
- 1999
(Show Context)
Citation Context ...a Ω(nk logk n) lower bound for degree k trees. In the distance model, in 1989, Hein [8] gave a Ω(n2 ) lower bound for reconstructing an arbitrary tree from additive distance data. In 1999, Kao et al. =-=[11]-=- claimed a Ω(n log n) lower bound for constructing binary trees from distance data with a flawed proof. For ultrametric distance data, they also give an Ω(deg(u) 2 + � v∈T \u(deg(v) − 1) 2 ) lower bou... |

3 |
T.: Tutorial on phylogenetic tree estimation. In: Intelligent Systems for Molecular Biology
- Kim, Warnow
- 1999
(Show Context)
Citation Context ... mutated independently according to the mutation matrix M(e). There are many ways to define M(e), from the simplest two character symmetric model (Cavender-Farris(CF) model, or two-state Neyman model =-=[4, 12]-=-) tothemost general model ([14, 2]). In our paper, we only consider the CF model as there is no inherent difficulty to go from the simplest to the most general model if we defineedgeweightsasin[2]. In... |

1 |
Efficient algorithms for δ )/ log γ. inverting evolution
- Farach, Kannan
- 1996
(Show Context)
Citation Context ...oblem of reconstructing trees when the distance information only approximates those in the true tree. Such problems arise naturally in DNA-based distance estimation methods. The methods, pioneered by =-=[6, 4]-=- and others, model the evolution as a stochastic process and use the DNA sequences to derive a measurement on the mutation distance between species on the tree. One can then apply distance-based metho... |

1 |
7 Conclusion a fast converging method for phylogenetic tree reconIn this paper, we first present a tight lower bound for distance-based evolutionary tree reconstruction. Then, we study the evolutionary tree reconstruction by using the bounded and restrict
- Disk-covering
- 1999
(Show Context)
Citation Context ... the bound to the so-called “edge-depth” rather than the diameter of the tree and thus reduced the DNA length needed from exponential to polynomial in terms of the number of species. A series of work =-=[4,5,9,3,2]-=- reduced the running time to O(n 2 ) [3] from the early high degree polynomial bound. In DNA-based distance estimation, if the distance between the sequences grows too large, the distance measure beco... |

1 |
On the complexity Both of our lower and upper bounds are related of distance-based evolutionary tree reconstruction. In to the tree cover size: the minimum number of leaves needed to cover all or a constant fraction of leaves. Our work therefore may motiv
- King, Zhang, et al.
- 2002
(Show Context)
Citation Context ... conclude with the proposal of some open problems and future work directions. Due to space constraint, we sketch some proofs in this extended abstract. For technical details, see our technical report =-=[13]-=-. 1.1 Related work Upper bounds: There has been extensive work on reconstruction of trees using relation and distance oracles with no error, beginning in 1977 with [15]. Optimal algorithms can be foun... |