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14
Treerank: A similarity measure for nearest neighbor searching in phylogenetic databases
 In Proceedings of the 15th International Conference on Scientific and Statistical Database Management
, 2003
"... Phylogenetic trees are unordered labeled trees in which each leaf node has a label and the order among siblings is unimportant. In this paper we propose a new similarity measure, called TreeRank, for phylogenetic trees and present an algorithm for computing TreeRank scores. Given a query tree ¥ or p ..."
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Cited by 19 (2 self)
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Phylogenetic trees are unordered labeled trees in which each leaf node has a label and the order among siblings is unimportant. In this paper we propose a new similarity measure, called TreeRank, for phylogenetic trees and present an algorithm for computing TreeRank scores. Given a query tree ¥ or pattern and a data tree, the TreeRank from ¥ to¦ score is a measure of the topological relationships that are found to be the same or similar. The proposed algorithm calculates in¥ the TreeRank score time where � is the in¦ number of nodes appearing both ¥ and¦ in and � , is the number of nodes. We then develop a search engine that, given a query or pattern in§©¨���������� and a database in¦ trees � of, finds and ranks the nearest of¥ tree¥ neighbors where the “nearness ” is measured by the proposed similarity function. This structurebased search engine is in� fully operational and is available on the World Wide Web. 1
Computing the quartet distance between evolutionary trees of bounded degree. Unpublished
, 2006
"... We present an algorithm for calculating the quartet distance between two evolutionary trees of bounded degree on a common set of n species. The previous best algorithm has running time O(d 2 n 2) when considering trees, where no node is of more than degree d. The algorithm developed herein has runni ..."
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Cited by 6 (2 self)
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We present an algorithm for calculating the quartet distance between two evolutionary trees of bounded degree on a common set of n species. The previous best algorithm has running time O(d 2 n 2) when considering trees, where no node is of more than degree d. The algorithm developed herein has running time O(d 9 n log n)) which makes it the first algorithm for computing the quartet distance between nonbinary trees which has a subquadratic worst case running time. 1.
Computing the quartet distance between trees of arbitrary degree
 In Proc. of WABI, volume 3692 of LNBI
, 2005
"... Comparing trees with regard to their topology is in itself an interesting theoretical problem in computer science, and furthermore researchers working in the interdisciplinary field of computational biology need tools to compare phylogenetic trees, i.e. trees that describe the relation of species ac ..."
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Cited by 4 (2 self)
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Comparing trees with regard to their topology is in itself an interesting theoretical problem in computer science, and furthermore researchers working in the interdisciplinary field of computational biology need tools to compare phylogenetic trees, i.e. trees that describe the relation of species according to evolutionary history. Different methods and different information can result in different phylogenetic trees, and consequently there is a need to be able to compare such trees. Comparison of trees can be done by calculating the distance between them, and among the distance measures usable on trees are the quartet distance. A quartet is a set of four leaves in a tree, and the edges in the tree connecting the leaves imply the topology of the quartet. The quartet distance between two trees containing the same leaves is the number of quartets containing the same four leaves that have different topology in the two trees. Previous algorithms focus on calculating the quartet distance between binary trees. We explore different approaches for calculating the quartet distance between trees of arbitrary degrees. Each approach gives rise to one or two algorithms with varying running times and space consumptions. The running times are verified experimentally and a possibility for reducing the space consumption of the fastest algorithm is discussed. We have implemented the fastest algorithm in a tool, which is also presented, along with the feature of visualizing the similarity of trees using the quartet distance. i Acknowledgments
Algorithms for computing the quartet distance between trees of arbitrary degree
 In Proc. of WABI, volume 3692 of LNBI
, 2005
"... Abstract. We present two algorithms for computing the quartet distance between trees of arbitrary degree. The quartet distance between two unrooted evolutionary trees is the number of quartets—subtrees induced by four leaves—that differs between the trees. Previous algorithms focus on computing the ..."
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Cited by 4 (2 self)
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Abstract. We present two algorithms for computing the quartet distance between trees of arbitrary degree. The quartet distance between two unrooted evolutionary trees is the number of quartets—subtrees induced by four leaves—that differs between the trees. Previous algorithms focus on computing the quartet distance between binary trees. In this paper, we present two algorithms for computing the quartet distance between trees of arbitrary degrees. One in time O(n 3) and space O(n 2) and one in time O(n 2 d 2) and space O(n 2), where n is the number of species and d is the maximal degree of the internal nodes of the trees. We experimentally compare the two algorithms and discuss possible directions for improving the running time further. 1
Efficient algorithms for descendent subtrees comparison of phylogenetic trees with applications to coevolutionary classifications in bacterial genome
 In The 14th Annual International Symposium on Algorithms and Computation (ISAAC’03), Lecture Notes in Computer Science 2906
, 2003
"... Abstract. A phylogenetic tree is a rooted tree with unbounded degree such that each leaf node is uniquely labelled from 1 to n. The descendent subtree of of a phylogenetic tree T is the subtree composed by all edges and nodes of T descending from a vertex. Given a set of phylogenetic trees, we prese ..."
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Cited by 1 (1 self)
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Abstract. A phylogenetic tree is a rooted tree with unbounded degree such that each leaf node is uniquely labelled from 1 to n. The descendent subtree of of a phylogenetic tree T is the subtree composed by all edges and nodes of T descending from a vertex. Given a set of phylogenetic trees, we present linear time algorithms for finding all leafagree descendent subtrees as well as all isomorphic descendent subtrees. The normalized cluster distance, d(A, B), of two sets is defined by d(A, B) = ∆(A, B)/(A  + B), where ∆(A, B) denotes the symmetric set difference of two sets. We show that computing all pairs normalized cluster distances between descendent subtrees of two phylogenetic trees can be done in O(n 2) time. Since the total size of the outputs will be Θ(n 2), the algorithm is thus computationally optimal. A nearest subtree of a subset of leaves is such a descendent subtree that has the smallest normalized cluster distance to these leaves. Here we show that finding nearest subtrees for a collection of pairwise disjointed subsets of leaves can be done in O(n) time. Several applications of these algorithms in areas of bioinformatics is considered. Among them, we discuss the 2CS (Two component systems) functional analysis and classifications on bacterial genome.
Computing the allpairs quartet distance on a set of evolutionary trees. Unpublished
, 2006
"... We present two algorithms for calculating the quartet distance between all pairs of trees in a set of binary evolutionary trees on a common set of species. The algorithms exploit common substructure among the trees to speed up the pairwise distance calculations thus performing significantly better o ..."
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Cited by 1 (1 self)
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We present two algorithms for calculating the quartet distance between all pairs of trees in a set of binary evolutionary trees on a common set of species. The algorithms exploit common substructure among the trees to speed up the pairwise distance calculations thus performing significantly better on large sets of trees compared to performing distinct pairwise distance calculations, as we illustrate experimentally, where we see a speedup factor of around 130 in the best case. 1.
Appendix for: Finding Patterns in Biological and Molecular Data
"... June 18, 2009This appendix contains all articles for which I have been a coauthor, in the order most relevant to the Progress Report. Contents: • Jesper Nielsen and Thomas Mailund: Snp le a software library and le format for large scale association mapping and population genetics studies. ..."
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June 18, 2009This appendix contains all articles for which I have been a coauthor, in the order most relevant to the Progress Report. Contents: • Jesper Nielsen and Thomas Mailund: Snp le a software library and le format for large scale association mapping and population genetics studies.
2 Association mapping 4
"... 2.1 Genetic variation............................ 4 2.2 Association mapping.......................... 4 ..."
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2.1 Genetic variation............................ 4 2.2 Association mapping.......................... 4
Visualization of Phylogenetic Trees
"... Abstract. We present a springembedder model for drawing rooted and unrooted phylogenetic trees with straight edges. Our heuristic strives for uniform edge lengths, and we develop it in analogy to forces in natural systems, for a simple, elegant, conceptually intuitive, and efficient algorithm. Thes ..."
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Abstract. We present a springembedder model for drawing rooted and unrooted phylogenetic trees with straight edges. Our heuristic strives for uniform edge lengths, and we develop it in analogy to forces in natural systems, for a simple, elegant, conceptually intuitive, and efficient algorithm. These algorithms are implemented on a webbased phylogeny visualization system that interoperates with existing tools developed for phylogenetic processing including CLUSTAL W, PHYLIP, PAUP. The molecular biologists can also manually construct their phylogenetic tree via existing system in, e.g., the Phylip format produced by CLUSTAL W as input format of the web system to which this data is to be fed.