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Reversal Distance without Hurdles and Fortresses [chapter]

Anne Bergeron, Julia Mixtacki, Jens Stoye
2004 Lecture Notes in Computer Science  
The parameters called 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.  ... 
doi:10.1007/978-3-540-27801-6_29 fatcat:cvawyxcqdzgk3ijxogqr7hbjja

An Algorithm to Enumerate Sorting Reversals for Signed Permutations

Adam C. Siepel
2003 Journal of Computational Biology  
Hannenhalli 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.  ... 
doi:10.1089/10665270360688200 pmid:12935346 fatcat:sd2dkca7qrcalozhm5wou76lyq

An algorithm to enumerate all sorting reversals

Adam C. Siepel
2002 Proceedings of the sixth annual international conference on Computational biology - RECOMB '02  
During the last decade, much progress was made both in computing 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  ... 
doi:10.1145/565196.565233 dblp:conf/recomb/Siepel02 fatcat:s7jkbojcm5c5hir4fyvl5qfojq

Transforming cabbage into turnip

Sridhar Hannenhalli, Pavel Pevzner
1995 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.  ... 
doi:10.1145/225058.225112 dblp:conf/stoc/HannenhalliP95 fatcat:jtirldcpafh2thhfgxqw7igrs4

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

Sridhar Hannenhalli, Pavel A. Pevzner
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.  ... 
doi:10.1145/300515.300516 fatcat:vbg6goklofhczo3bwy76ecrxey

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

Niklas Eriksen
2002 Theoretical Computer Science  
We present a (1 + )-approximation for this problem, based on the exact algorithm of Hannenhalli 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.  ... 
doi:10.1016/s0304-3975(01)00338-3 fatcat:o63duy6fgbejjkwrcxvdjlmxlm

Parallel Algorithms for Reversal Distance of Permutations on PRAM and LARPBS

2007 Journal of Software (Chinese)  
This paper presents two parallel algorithms to compute 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).  ... 
doi:10.1360/jos182683 fatcat:koiy2edtbzbebfzqkolynrufby

(1+ε)-Approximation of Sorting by Reversals and Transpositions [chapter]

Niklas Eriksen
2001 Lecture Notes in Computer Science  
Strong super 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.  ... 
doi:10.1007/3-540-44696-6_18 fatcat:f7kz5je5ozform36mcjnv2nx4u

Hurdles and Sorting by Inversions: Combinatorial, Statistical, and Experimental Results

Krister M. Swenson, Yu Lin, Vaibhav Rajan, Bernard M.E. Moret
2009 Journal of Computational Biology  
The characterization relies on the concepts of breakpoints, cycles, 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  ... 
doi:10.1089/cmb.2009.0156 pmid:19747037 fatcat:owfgmvfueza2bn76vspvtfwwpm

Heuristic Algorithm for Computing Reversal Distance with MultiGene Families via Binary Integer Programming

J. Suksawatchon, C. Lursinsap, M. Boden
2005 2005 IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology  
The experimental results on simulated 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.  ... 
doi:10.1109/cibcb.2005.1594916 fatcat:yr7ygrxju5cwdjg6ccvxep7q6q

Common intervals and sorting by reversals: a marriage of necessity

A. Bergeron, S. Heber, J. Stoye
2002 Bioinformatics  
Mixing the two approaches yields new definitions 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.  ... 
doi:10.1093/bioinformatics/18.suppl_2.s54 pmid:12385983 fatcat:ts3t7vlkovf4zmjyrrqvngxxre

Algorithmic approaches for genome rearrangement: a review

Zimao Li, Lusheng Wang, Kaizhong Zhang
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 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  ... 
doi:10.1109/tsmcc.2005.855522 fatcat:gozisli5bve7dibqpukmtwejtm

Assignment of Orthologous Genes via Genome Rearrangement

Xin Chen, Jie Zheng, Zheng Fu, Peng Nan, Yang Zhong, S. Lonardi, Tao Jiang
2005 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 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.  ... 
doi:10.1109/tcbb.2005.48 pmid:17044168 fatcat:vqqt3fu7drbypmxgs6b6ncfk44

Efficient Sampling of Parsimonious Inversion Histories with Application to Genome Rearrangement in Yersinia

István Miklós, Aaron E. Darling
2009 Genome Biology and Evolution  
Inversions are among the most common mutations acting on the order 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.  ... 
doi:10.1093/gbe/evp015 pmid:20333186 pmcid:PMC2817410 fatcat:pvw2euu7onf7lij7oh522modla

Estimating the expected reversal distance after a fixed number of reversals

Niklas Eriksen, Axel Hultman
2004 Advances in Applied Mathematics  
We address the problem of computing the expected 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.  ... 
doi:10.1016/s0196-8858(03)00054-x fatcat:uorjocbedbbvdjgzjtugijavxe
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