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Reversal Distance without Hurdles and Fortresses
[chapter]

2004
*
Lecture Notes in Computer Science
*

The parameters called

doi:10.1007/978-3-540-27801-6_29
fatcat:cvawyxcqdzgk3ijxogqr7hbjja
*hurdles**and**fortress*are replaced by a single one, whose value is computed by a simple*and*efficient algorithm. ... This paper presents an elementary proof of the Hannenhalli-Pevzner theorem on the*reversal**distance*of two signed permutations. ... In this paper, we show that simple results on trees are at the root of all results on*hurdles*, either maximal or simple, super-*hurdles*,*and**fortresses*. ...##
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An Algorithm to Enumerate Sorting Reversals for Signed Permutations

2003
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Journal of Computational Biology
*

Hannenhalli

doi:10.1089/10665270360688200
pmid:12935346
fatcat:sd2dkca7qrcalozhm5wou76lyq
*and*Pevzner proved that*reversal**distance*can be exactly expressed as a function of the numbers of cycles,*hurdles*,*and**fortresses**and*derived a O.n 4 /-time algorithm to sort by*reversals*... Recently, Bader, Moret,*and*Yan (2001) have shown how to compute*reversal**distance*(*without*actually sorting) in O.n/ time,*and*Bergeron (2001)*and*Bergeron*and*Strasbourg (2001) have described an alternative ... it u,*without*loss of generality-*and*the other, v, is a nonhurdle that is separated from u by a second*hurdle*. ...##
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An algorithm to enumerate all sorting reversals

2002
*
Proceedings of the sixth annual international conference on Computational biology - RECOMB '02
*

During the last decade, much progress was made both in computing

doi:10.1145/565196.565233
dblp:conf/recomb/Siepel02
fatcat:s7jkbojcm5c5hir4fyvl5qfojq
*reversal**distance**and*in finding a minimum sequence of sorting*reversals*. ... The problem of estimating evolutionary*distance*from differences in gene order has been distilled to the problem of finding the*reversal**distance*between two signed permutations. ... ACKNOWLEDGEMENTS Thanks to Bernard Moret, the author's adviser at the University of New Mexico, for encouragement*and*support,*and*to the anonymous reviewers of this paper for corrections*and*helpful suggestions ...##
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Transforming cabbage into turnip

1995
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Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95
*

*Reversal*

*distance*between permutations

*and*is the minimum number of

*reversals*to transform into . ... The previously suggested approximation algorithms for sorting signed permutations by

*reversals*compute the

*reversal*

*distance*between permutations with an astonishing accuracy for both simulated

*and*biological ... We are indebted to Vineet Bafna, Piotr Berman, Webb Miller,

*and*Anatoly Rubinov for many helpful discussions

*and*suggestions. ...

##
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Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals

1999
*
Journal of the ACM
*

*Reversal*

*distance*between permutations

*and*is the minimum number of

*reversals*to transform into . ... The previously suggested approximation algorithms for sorting signed permutations by

*reversals*compute the

*reversal*

*distance*between permutations with an astonishing accuracy for both simulated

*and*biological ... We are indebted to Vineet Bafna, Piotr Berman, Webb Miller,

*and*Anatoly Rubinov for many helpful discussions

*and*suggestions. ...

##
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(1+ε)-Approximation of sorting by reversals and transpositions

2002
*
Theoretical Computer Science
*

We present a (1 + )-approximation for this problem, based on the exact algorithm of Hannenhalli

doi:10.1016/s0304-3975(01)00338-3
fatcat:o63duy6fgbejjkwrcxvdjlmxlm
*and*Pevzner for sorting by*reversals*only. ... Gu et al. gave a 2-approximation for computing the minimal number of inversions*and*transpositions needed to sort a permutation. ... Niklas Eriksen was supported by the Swedish Natural Science Research Council*and*the Swedish Foundation for Strategic Research. ...##
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Parallel Algorithms for Reversal Distance of Permutations on PRAM and LARPBS

2007
*
Journal of Software (Chinese)
*

This paper presents two parallel algorithms to compute

doi:10.1360/jos182683
fatcat:koiy2edtbzbebfzqkolynrufby
*reversal**distance*of two signed permutations on different models. ... of*hurdles*in break point graph. ... Determine whether breakpoint graph B(π) is a*fortress*f(π)*and*compute the*reversal**distance*of π, d(π)=n−c(π)+h(π)+f(π). 1≤i≤n, we join vertices a 2i*and*a 2i+1 by a black edge (9~11). ...##
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(1+ε)-Approximation of Sorting by Reversals and Transpositions
[chapter]

2001
*
Lecture Notes in Computer Science
*

Strong super

doi:10.1007/3-540-44696-6_18
fatcat:f7kz5je5ozform36mcjnv2nx4u
*hurdles**and*strong*fortresses*are defined in the same way as super*hurdles**and**fortresses*(just replace*hurdle*with strong*hurdle*). ... If we have an odd number of super*hurdles**and*no other*hurdles*, the permutation is known as a*fortress*. ...##
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Hurdles and Sorting by Inversions: Combinatorial, Statistical, and Experimental Results

2009
*
Journal of Computational Biology
*

The characterization relies on the concepts of breakpoints, cycles,

doi:10.1089/cmb.2009.0156
pmid:19747037
fatcat:owfgmvfueza2bn76vspvtfwwpm
*and*obstructions colorfully named*hurdles**and**fortresses*. ... One of the main rearrangement mechanisms, inversions (also called*reversals*), was characterized by Hannenhalli*and*Pevzner*and*this characterization in turn extended by various authors. ... THE RARITY OF*HURDLES**AND**FORTRESSES*In this section, we provide asymptotic characterizations in Y( ) terms of the probability that a*hurdle*or*fortress*is found in a signed permutation selected uniformly ...##
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Heuristic Algorithm for Computing Reversal Distance with MultiGene Families via Binary Integer Programming

2005
*
2005 IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology
*

The experimental results on simulated

doi:10.1109/cibcb.2005.1594916
fatcat:yr7ygrxju5cwdjg6ccvxep7q6q
*and*real biological data demonstrate that the proposed algorithm is able to find the*reversal**distance*accurately. ... We propose a new heuristic algorithm to compute the*reversal**distance*between two genomes with multigene families via the concept of binary integer programming*without*removing gene duplicates. ... A*fortress*exists iff there is an odd number of*hurdles**and*all are superhurdles. ...##
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Common intervals and sorting by reversals: a marriage of necessity

2002
*
Bioinformatics
*

Mixing the two approaches yields new definitions

doi:10.1093/bioinformatics/18.suppl_2.s54
pmid:12385983
fatcat:ts3t7vlkovf4zmjyrrqvngxxre
*and*algorithms for the*reversal**distance*computations, that apply directly on the original permutation. ... This paper revisits the problem of sorting by*reversals*with tools developed in the context of detecting common intervals. ... The main problem in computing the*reversal**distance*is thus the classification of unoriented components as*hurdles*, super-*hurdles*,*and*non-*hurdles*. ...##
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Algorithmic approaches for genome rearrangement: a review

2006
*
IEEE Transactions on Systems Man and Cybernetics Part C (Applications and Reviews)
*

In this paper, we cover many kinds of rearrangement events such as

doi:10.1109/tsmcc.2005.855522
fatcat:gozisli5bve7dibqpukmtwejtm
*reversal*, transposition, translocation, fussion, fission,*and*so on. ... Different types of*distances*between genomes or chromosomes are discussed. A variety of mathematic models are included. ... If π is*fortress*then a sequence of k − 1*reversals*merging pairs of nonconsecutive*hurdles*followed by two additional merges of pairs of consecutive*hurdles*(one merges two original*hurdles**and*the next ...##
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Assignment of Orthologous Genes via Genome Rearrangement

2005
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IEEE/ACM Transactions on Computational Biology & Bioinformatics
*

The simulation results demonstrate that SOAR in general performs better than the iterated exemplar algorithm in terms of computing the

doi:10.1109/tcbb.2005.48
pmid:17044168
fatcat:vqqt3fu7drbypmxgs6b6ncfk44
*reversal**distance**and*assigning correct orthologs. ... First, the problem is formulated as that of computing the signed*reversal**distance*with duplicates between the two genomes of interest. ... This project is supported in part by NSF grants ITR-0085910, CCR-0309902,*and*DBI-0321756, a DOE Genomics:GTL subcontract,*and*National Key Project for Basic Research (973) grant 2002CB512801. ...##
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Efficient Sampling of Parsimonious Inversion Histories with Application to Genome Rearrangement in Yersinia

2009
*
Genome Biology and Evolution
*

Inversions are among the most common mutations acting on the order

doi:10.1093/gbe/evp015
pmid:20333186
pmcid:PMC2817410
fatcat:pvw2euu7onf7lij7oh522modla
*and*orientation of genes in a genome,*and*polynomial-time algorithms exist to obtain a minimal length series of inversions that transform ... We find that on high-divergence data sets, MC4Inversion finds more optimal sorting paths per second than BADGER*and*the IS technique*and*simultaneously avoids bias inherent in the IS technique. ... , h(z) is the number of*hurdles*in z,*and*f(z) is 1 if z is a*fortress*, otherwise 0. ...##
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Estimating the expected reversal distance after a fixed number of reversals

2004
*
Advances in Applied Mathematics
*

We address the problem of computing the expected

doi:10.1016/s0196-8858(03)00054-x
fatcat:uorjocbedbbvdjgzjtugijavxe
*reversal**distance*of a genome with n genes obtained by applying t random*reversals*to the identity. ... A good approximation is the expected transposition*distance*of a product of t random transpositions in S n . ... Finally, if a breakpoint graph contains an odd number of*hurdles*, all of which are super*hurdles*, then this graph is known as a*fortress*. ...
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