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35
On the Similarity of Sets of Permutations and its Applications to Genome Comparison
, 2003
"... The comparison of genomes with the same gene content relies on our ability to compare permutations, either by measuring how much they di#er, or by measuring how much they are alike. With the notable exception of the breakpoint distance, which is based on the concept of conserved adjacencies, meas ..."
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Cited by 41 (8 self)
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The comparison of genomes with the same gene content relies on our ability to compare permutations, either by measuring how much they di#er, or by measuring how much they are alike. With the notable exception of the breakpoint distance, which is based on the concept of conserved adjacencies, measures of distance do not generalize easily to sets of more than two permutations. In this paper, we present a basic unifying notion, conserved intervals, as a powerful generalization of adjacencies, and as a key feature of genome rearrangement theories. We also show that sets of conserved intervals have elegant nesting and chaining properties that allow the development of compact graphic representations, and linear time algorithms to manipulate them.
Computing common intervals of K permutations, with applications to modular decomposition of graphs
, 2008
"... We introduce a new approach to compute the common intervals of K permutations based on a very simple and general notion of generators of common intervals. This formalism leads to simple and efficient algorithms to compute the set of all common intervals of K permutations, that can contain a quadrat ..."
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Cited by 33 (13 self)
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We introduce a new approach to compute the common intervals of K permutations based on a very simple and general notion of generators of common intervals. This formalism leads to simple and efficient algorithms to compute the set of all common intervals of K permutations, that can contain a quadratic number of intervals, as well as a linear space basis of this set of common intervals. Finally, we show how our results on permutations can be used for computing the modular decomposition of graphs.
The Algorithmic of Gene Teams
, 2002
"... Comparative genomics is a growing field in computational biology, and one of its typical problem is the identification of sets of orthologous genes that have virtually the same function in several genomes. ..."
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Cited by 30 (7 self)
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Comparative genomics is a growing field in computational biology, and one of its typical problem is the identification of sets of orthologous genes that have virtually the same function in several genomes.
Perfect sorting by reversals is not always difficult
 IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS
, 2007
"... We propose new algorithms for computing pairwise rearrangement scenarios that conserve the combinatorial structure of genomes. More precisely, we investigate the problem of sorting signed permutations by reversals without breaking common intervals. We describe a combinatorial framework for this prob ..."
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Cited by 26 (11 self)
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We propose new algorithms for computing pairwise rearrangement scenarios that conserve the combinatorial structure of genomes. More precisely, we investigate the problem of sorting signed permutations by reversals without breaking common intervals. We describe a combinatorial framework for this problem that allows us to characterize classes of signed permutations for which one can compute, in polynomial time, a shortest reversal scenario that conserves all common intervals. In particular, we define a class of permutations for which this computation can be done in linear time with a very simple algorithm that does not rely on the classical HannenhalliPevzner theory for sorting by reversals. We apply these methods to the computation of rearrangement scenarios between permutations obtained from 16 synteny blocks of the X chromosomes of the human, mouse, and rat.
Tests for Gene Clustering
, 2002
"... Comparing chromosomal gene order in two or more related species is an important approach to studying the forces that guide genome organization and evolution. Linked clusters of similar genes found in related genomes are often used to support arguments of evolutionary relatedness or functional select ..."
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Cited by 26 (3 self)
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Comparing chromosomal gene order in two or more related species is an important approach to studying the forces that guide genome organization and evolution. Linked clusters of similar genes found in related genomes are often used to support arguments of evolutionary relatedness or functional selection. However, as the gene order and the gene complement of sister genomes diverge progressively due to large scale rearrangements, horizontal gene transfer, gene duplication and gene loss, it becomes increasingly difficult to determine whether observed similarities in local genomic structure are indeed remnants of common ancestral gene order, or are merely coincidences.
Quadratic time algorithms for finding common intervals in two and more sequences
 In Proceedings of the 15th Annual Symposium on Combinatorial Pattern Matching, CPM 2004, volume 3109 of LNCS
, 2004
"... Abstract. A popular approach in comparative genomics is to locate groups or clusters of orthologous genes in multiple genomes and to postulate functional association between the genes contained in such clusters. To this end, genomes are often represented as permutations of their genes, and common in ..."
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Cited by 21 (6 self)
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Abstract. A popular approach in comparative genomics is to locate groups or clusters of orthologous genes in multiple genomes and to postulate functional association between the genes contained in such clusters. To this end, genomes are often represented as permutations of their genes, and common intervals, i.e. intervals containing the same set of genes, are interpreted as gene clusters. A disadvantage of modelling genomes as permutations is that paralogous copies of the same gene inside one genome can not be modelled. In this paper we consider a slightly modified model that allows paralogs, simply by representing genomes as sequences rather than permutations of genes. We define common intervals based on this model, and we present a simple algorithm that finds all common intervals of two sequences in Θ(n 2) time using Θ(n 2) space. Another, more complicated algorithm runs in O(n 2) time and uses only linear space. We also show how to extend the simple algorithm to more than two genomes, and we present results from the application of our algorithms to real data. 1
Revisiting T. Uno and M. Yagiura’s algorithm
 Proc. 16th International Symposium on Algorithms and Computation, in Lecture Notes in Comput. Sci
, 2005
"... Abstract. In 2000, T. Uno and M. Yagiura published an algorithm that computes all the K common intervals of two given permutations of length n in O(n + K) time. Our paper first presents a decomposition approach to obtain a compact encoding for common intervals of d permutations. Then, we revisit T. ..."
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Cited by 20 (6 self)
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Abstract. In 2000, T. Uno and M. Yagiura published an algorithm that computes all the K common intervals of two given permutations of length n in O(n + K) time. Our paper first presents a decomposition approach to obtain a compact encoding for common intervals of d permutations. Then, we revisit T. Uno and M. Yagiura’s algorithm to yield a linear time algorithm for finding this encoding. Besides, we adapt the algorithm to obtain a linear time modular decomposition of an undirected graph, and thereby propose a formal invariantbased proof for all these algorithms. 1
Gene proximity analysis across whole genomes via PQ trees
 Journal of Computational Biology
, 2005
"... Permutations on strings representing gene clusters on genomes have been studied earlier ..."
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Cited by 17 (0 self)
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Permutations on strings representing gene clusters on genomes have been studied earlier
Gene Teams: A New Formalization of Gene Clusters for Comparative Genomics
"... This paper describes an efficient algorithm based on a new concept called gene team for detecting conserved gene clusters among an arbitrary number of chromosomes. Within the clusters, neither the order of the genes nor their orientation need be conserved. In addition, insertion of foreign genes ..."
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Cited by 12 (2 self)
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This paper describes an efficient algorithm based on a new concept called gene team for detecting conserved gene clusters among an arbitrary number of chromosomes. Within the clusters, neither the order of the genes nor their orientation need be conserved. In addition, insertion of foreign genes within the clusters are permitted to a userdefined extent. This algorithm has been implemented in a publicly available TEAM software, that proves to be an efficient tool for systematic searches of conserved gene clusters. Examples of actual biological results are provided. The software is downloadable from http://wwwigm.univmlv.fr/~raffinot/geneteam.html .
Algorithms for Finding Gene Clusters
, 2001
"... Comparing gene orders in completely sequenced genomes is a standard approach to locate clusters of functionally associated genes. ..."
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Cited by 11 (2 self)
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Comparing gene orders in completely sequenced genomes is a standard approach to locate clusters of functionally associated genes.