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A Lower Bound on the Reversal and Transposition Diameter
, 2000
"... One possible model to study genome evolution is to represent genomes as permutations of genes and compute distances based on the minimum number of certain operations (rearrangements) needed to transform one permutation into another. Under this model, the shorter the distance, the closer the genom ..."
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Cited by 4 (0 self)
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the genomes are. Two operations that have been extensively studied are the reversal and the transposition. A reversal is an operation that reverses the order of the genes on a certain portion of the permutation. A transposition is an operation that \cuts" a certain portion of the permutation
An Approximation Algorithm for Sorting by Reversals and Transpositions
"... Abstract. Genome rearrangement algorithms are powerful tools to analyze gene orders in molecular evolution. Analysis of genomes evolving by reversals and transpositions leads to a combinatorial problem of sorting by reversals and transpositions, the problem of finding a shortest sequence of reversal ..."
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of k our approximation ratio becomes 2.5909 + δ for any δ> 0. We also derive a lower bound on reversal and transposition distance of an unsigned permutation. 1
Lower bounding edit distances between permutations
, 2013
"... A number of fields, including the study of genome rearrangements and the design of interconnection networks, deal with the connected problems of sorting permutations in “as few moves as possible”, using a given set of allowed operations, or computing the number of moves the sorting process requires, ..."
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to improve the best known lower bound on the prefix transposition diameter from 2n/3 to ⌊3n/4⌋, and investigate a few relations between some statistics on π and π.
Asymptotically Tight Bounds for Performing BMMC Permutations on Parallel Disk Systems
, 1994
"... This paper presents asymptotically equal lower and upper bounds for the number of parallel I/O operations required to perform bitmatrixmultiply/complement (BMMC) permutations on the Parallel Disk Model proposed by Vitter and Shriver. A BMMC permutation maps a source index to a target index by an a ..."
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Cited by 55 (18 self)
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This paper presents asymptotically equal lower and upper bounds for the number of parallel I/O operations required to perform bitmatrixmultiply/complement (BMMC) permutations on the Parallel Disk Model proposed by Vitter and Shriver. A BMMC permutation maps a source index to a target index
A BranchandBound Method for the Multichromosomal Reversal Median Problem
"... Abstract. The ordering of genes in a genome can be changed through rearrangement events such as reversals, transpositions and translocations. Since these rearrangements are “rare events”, they can be used to infer deep evolutionary histories. One important problem in rearrangement analysis is to fin ..."
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solver, at least on unichromosomal genomes. In this paper, we present a new branchandbound method that provides an exact solution to the multichromosomal reversal median problem. We develop tight lower bounds and improve the enumeration procedure such that the search can be performed efficiently. Our extensive
Edit Distances and Factorisations of Even Permutations
"... Abstract. A number of fields, including genome rearrangements and interconnection network design, are concerned with sorting permutations in “as few moves as possible”, using a given set of allowed operations. These often act on just one or two segments of the permutation, e.g. by reversing one segm ..."
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Cited by 5 (3 self)
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of particular factorisations of the latter permutation. Using our framework, we recover known results in a simple and unified way, and obtain a new lower bound on the prefix transposition distance (where a prefix transposition displaces the initial segment of a permutation), which is shown to outperform
Approximation algorithms for genome rearrangements (sorting signed . . .
 IN PROC. OF THE 7TH WORKSHOP ON GENOME INFORMATICS
, 1996
"... Recently, a new approach to analyze genomes evolving was proposed which is based on comparison of gene orders versus traditional comparison of DNA sequences (Sanko et al, 1992). The approach is based on the global rearrangements (e.g., inversions and transpositions of fragments). Analysis of genomes ..."
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Cited by 10 (2 self)
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by reversals and transpositions, a problem which adequately models genome rearrangements, as the genes in DNA are oriented. We establish a lower bound and give two algorithms for the problem. Based on the lower bound, we show that the rst algorithm is a 2approximation algorithm. The time complexity
A lemma and a conjecture on the cost of rearrangements
 Rend. Sem. Mat. Univ. Padova
"... Consider a stack of books, containing both white and black books. Suppose that we want to sort them out, putting the white books on the right, and the black books on the left (fig. 1). This will be done by a finite sequence of elementary transpositions. In other words, if we have a stack of all blac ..."
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black books of length a followed by a stack of all white books of length b, we are allowed to reverse their order at the cost of a + b. We are interested in a lower bound on the total cost of the rearrangement. Assume that initially the white and black books are highly mixed. By this we mean that inside
Sorting Primitives and Genome Rearrangement in Bioinformatics: A Unified Perspective
, 2008
"... Bioinformatics and computational biology involve the use of techniques including applied mathematics, informatics, statistics, computer science, artificial intelligence, chemistry, and biochemistry to solve biological problems usually on the molecular level. Research in computational biology often ..."
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rearrangements of permutations, such as reversals and transpositions,have recently become of interest because of their applications in computational molecular biology. A reversal is an operation that reverses the order of a substring of a permutation. A transposition is an operation that swaps two adjacent
MultiBreak Rearrangements: from Circular to Linear Genomes
 Lecture Notes in Bioinformatics 4751
, 2007
"... Abstract. Multibreak rearrangements break a genome into multiple fragments and further glue them together in a new order. While 2break rearrangements represent standard reversals, fusions, fissions, and translocations operations; 3break rearrangements are a natural generalization of transpositions ..."
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Abstract. Multibreak rearrangements break a genome into multiple fragments and further glue them together in a new order. While 2break rearrangements represent standard reversals, fusions, fissions, and translocations operations; 3break rearrangements are a natural generalization
Results 1  10
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