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Towards Optimal Distance Functions for Stochastic Substitutions Models
, 2009
"... Distance based reconstruction methods of phylogenetic trees consist of two independent parts: first, interspecies distances are inferred assuming some stochastic model of sequence evolution; then the inferred distances are used to construct a tree. In this paper we concentrate on the task of inters ..."
Abstract

Cited by 6 (4 self)
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Distance based reconstruction methods of phylogenetic trees consist of two independent parts: first, interspecies distances are inferred assuming some stochastic model of sequence evolution; then the inferred distances are used to construct a tree. In this paper we concentrate on the task of interspecies distance estimation. Specifically, we characterize the family of valid distance functions for the assumed substitution model and show that deliberate selection of distance function significantly improves the accuracy of distance estimates and, consequently, also improves the accuracy of the reconstructed tree. Our contribution consists of three parts: First, we present a general framework for constructing families of additive distance functions for stochastic evolutionary models. Then, we present a method for selecting (near) optimal distance functions, and we conclude by presenting simulation results which support our theoretical analysis. 1 Introduction. One of the most popular approaches to phylogenetic reconstruction is the distance based approach. This approach associates lengths to the edges of the phylogenetic tree. The additive distance between two
Fast and reliable reconstruction of phylogenetic trees with very short edges
 In SODA: ACMSIAM Symposium on Discrete Algorithms
, 2008
"... Phylogenetic reconstruction is the problem of reconstructing an evolutionary tree from sequences corresponding to leaves of that tree. A central goal in phylogenetic reconstruction is to be able to reconstruct the tree as accurately as possible from as short as possible input sequences. The sequence ..."
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Cited by 6 (2 self)
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Phylogenetic reconstruction is the problem of reconstructing an evolutionary tree from sequences corresponding to leaves of that tree. A central goal in phylogenetic reconstruction is to be able to reconstruct the tree as accurately as possible from as short as possible input sequences. The sequence length required for correct topological reconstruction depends on certain properties of the tree, such as its depth and minimal edgeweight. Fast converging reconstruction algorithms are considered stateof theart in this sense, as they require asymptotically minimal sequence length in order to guarantee (with high probability) correct topological reconstruction of the entire tree. However, when the original phylogenetic tree contains very short edges, this minimal sequencelength is still too long for practical purposes. Short
Optimal implementations of UPGMA and other common clustering algorithms
, 2007
"... In this work we consider hierarchical clustering algorithms, such as UPGMA, which follow the closestpair joining scheme. We study optimal O(n 2)time implementations of such algorithms which use a ‘locally closest ’ joining scheme, and specify conditions under which this relaxed joining scheme is e ..."
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Cited by 4 (1 self)
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In this work we consider hierarchical clustering algorithms, such as UPGMA, which follow the closestpair joining scheme. We study optimal O(n 2)time implementations of such algorithms which use a ‘locally closest ’ joining scheme, and specify conditions under which this relaxed joining scheme is equivalent to the original one (i.e. ‘globally closest’). Key Words: Hierarchical clustering, UPGMA, design of algorithms, inputoutput specification, computational complexity
On The Hardness of Inferring Phylogenies from TripletDissimilarities
, 2007
"... This work considers the problem of reconstructing a phylogenetic tree from triplet dissimilarities, which are dissimilarities defined over taxontriplets. Triplet dissimilarities are possibly the simplest generalization of pairwise dissimilarities, and were used for phylogenetic reconstructions in th ..."
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This work considers the problem of reconstructing a phylogenetic tree from triplet dissimilarities, which are dissimilarities defined over taxontriplets. Triplet dissimilarities are possibly the simplest generalization of pairwise dissimilarities, and were used for phylogenetic reconstructions in the past few years. We study the hardness of finding a tree best fitting a given tripletdissimilarity table under the ℓ ∞ norm. We show that the corresponding decision problem is NPhard and that the corresponding optimization problem cannot be approximated in polynomial time within a constant multiplicative factor smaller than 1.4. On the positive side, we present a polynomial time constantrate approximation algorithm for this problem. We also address the issue of bestfit under maximal distortion, which corresponds to the largest ratio between matching entries in two tripletdissimilarity tables. We show that it is NPhard to approximate the corresponding optimization problem within any constant multiplicative factor. 1