The complexity of finding minimum-length generator sequences
Theoretical Computer Science
Sorting by insertion of leading elements
Journal of Combinatorial Theory Series A
Sorting by reversals is difficult
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
SIAM Journal on Discrete Mathematics
Of mice and men: algorithms for evolutionary distances between genomes with translocation
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
To cut…or not to cut (applications of comparative physical maps in molecular evolution)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Faster and simpler algorithm for sorting signed permutations by reversals
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Reconstructing a history of recombinations from a set of sequences
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Genome Rearrangements and Sorting by Reversals
SIAM Journal on Computing
Edit Distances for Genome Comparisons Based on Non-Local Operations
CPM '92 Proceedings of the Third Annual Symposium on Combinatorial Pattern Matching
Efficient Bounds for Oriented Chromosome Inversion Distance
CPM '94 Proceedings of the 5th Annual Symposium on Combinatorial Pattern Matching
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
Transforming men into mice (polynomial algorithm for genomic distance problem)
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Open Combinatorial Problems in computational Molecular Biology
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Efficient algorithms for multichromosomal genome rearrangements
Journal of Computer and System Sciences - Computational biology 2002
On the Practical Solution of the Reversal Median Problem
WABI '01 Proceedings of the First International Workshop on Algorithms in Bioinformatics
Algorithms for Finding Gene Clusters
WABI '01 Proceedings of the First International Workshop on Algorithms in Bioinformatics
Experiments in Computing Sequences of Reversals
WABI '01 Proceedings of the First International Workshop on Algorithms in Bioinformatics
Sorting by Prefix Transpositions
SPIRE 2002 Proceedings of the 9th International Symposium on String Processing and Information Retrieval
A Very Elementary Presentation of the Hannenhalli-Pevzner Theory
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
A new approximation algorithm for sorting of signed permutations
Journal of Computer Science and Technology
Chromosomal breakpoint re-use in the inference of genome sequence rearrangement
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Improved bounds on sorting with length-weighted reversals
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
On maximal instances for the original syntenic distance
Theoretical Computer Science
An O(n2) algorithm for signed translocation
Journal of Computer and System Sciences - Special issue on bioinformatics II
A 1.5-approximation algorithm for sorting by transpositions and transreversals
Journal of Computer and System Sciences - Special issue on bioinformatics II
Sorting signed permutations by reversals, revisited
Journal of Computer and System Sciences - Special issue on bioinformatics II
On the complexity of unsigned translocation distance
Theoretical Computer Science
New Bounds and Tractable Instances for the Transposition Distance
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A 1.375-Approximation Algorithm for Sorting by Transpositions
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Approximating reversal distance for strings with bounded number of duplicates
Discrete Applied Mathematics
Advances on sorting by reversals
Discrete Applied Mathematics
Perfect Sorting by Reversals Is Not Always Difficult
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Colored de Bruijn Graphs and the Genome Halving Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Reversal and transposition medians
Theoretical Computer Science
A very elementary presentation of the Hannenhalli-Pevzner theory
Discrete Applied Mathematics - 12th annual symposium on combinatorial pattern matching (CPM)
Evolution under Reversals: Parsimony and Conservation of Common Intervals
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Faster algorithms for sorting by transpositions and sorting by block interchanges
ACM Transactions on Algorithms (TALG)
Whole genome duplications, multi-break rearrangements, and genome halving problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A linear time algorithm for the inversion median problem in circular bacterial genomes
Journal of Discrete Algorithms
Comparing bacterial genomes from linear orders of patterns
Discrete Applied Mathematics
Sequential vs. parallel complexity in simple gene assembly
Theoretical Computer Science
Information Processing Letters
Consensus Genetic Maps as Median Orders from Inconsistent Sources
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Improved bounds on sorting by length-weighted reversals
Journal of Computer and System Sciences
Expected number of breakpoints after t random reversals in genomes with duplicate genes
Discrete Applied Mathematics
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Multichromosomal Genome Median and Halving Problems
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
Decompositions of Multiple Breakpoint Graphs and Rapid Exact Solutions to the Median Problem
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
RECOMB-CG '08 Proceedings of the international workshop on Comparative Genomics
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
The gene evolution model and computing its associated probabilities
Journal of the ACM (JACM)
Approximability and Fixed-Parameter Tractability for the Exemplar Genomic Distance Problems
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Polynomial-Time Algorithm for Sorting by Generalized Translocations
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Average-Case Analysis of Perfect Sorting by Reversals
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
A new linear time algorithm to compute the genomic distance via the double cut and join distance
Theoretical Computer Science
Rearrangement Models and Single-Cut Operations
RECOMB-CG '09 Proceedings of the International Workshop on Comparative Genomics
A very elementary presentation of the Hannenhalli-Pevzner theory
Discrete Applied Mathematics
A simpler and faster 1.5-approximation algorithm for sorting by transpositions
Information and Computation
An improved algorithm for sorting by block-interchanges based on permutation groups
Information Processing Letters
On the similarity of sets of permutations and its applications to genome comparison
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
The solution space of sorting by reversals
ISBRA'07 Proceedings of the 3rd international conference on Bioinformatics research and applications
Prefix reversals on binary and ternary strings
AB'07 Proceedings of the 2nd international conference on Algebraic biology
Characterizing reduction graphs for gene assembly in ciliates
DLT'07 Proceedings of the 11th international conference on Developments in language theory
How to achieve an equivalent simple permutation in linear time
RECOMB-CG'07 Proceedings of the 2007 international conference on Comparative genomics
Evolution of tandemly arrayed genes in multiple species
RECOMB-CG'07 Proceedings of the 2007 international conference on Comparative genomics
On the cost of interchange rearrangement in strings
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Sorting Genomes by Reciprocal Translocations, Insertions, and Deletions
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Reactive stochastic local search algorithms for the genomic median problem
EvoCOP'08 Proceedings of the 8th European conference on Evolutionary computation in combinatorial optimization
Decoding synteny blocks and large-scale duplications in mammalian and plant genomes
WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
A fixed-parameter algorithm for string-to-string correction
CATS '10 Proceedings of the Sixteenth Symposium on Computing: the Australasian Theory - Volume 109
Breakpoint distance and PQ-trees
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Listing all sorting reversals in quadratic time
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Advances on genome duplication distances
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
On sorting genomes with DCJ and indels
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
On exploring genome rearrangement phylogenetic patterns
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
Polynomial-time sortable stacks of burnt pancakes
Theoretical Computer Science
Sorting unsigned permutations by weighted reversals, transpositions, and transreversals
Journal of Computer Science and Technology
On the Cost of Interchange Rearrangement in Strings
SIAM Journal on Computing
A polynomial algebra method for computing exemplar breakpoint distance
ISBRA'11 Proceedings of the 7th international conference on Bioinformatics research and applications
Discrete Applied Mathematics
Quick greedy computation for minimum common string partitions
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
An O(n3/2log(n)) algorithm for sorting by reciprocal translocations
Journal of Discrete Algorithms
A Lower Bound on the Transposition Diameter
SIAM Journal on Discrete Mathematics
Maximizing synteny blocks to identify ancestral homologs
RCG'05 Proceedings of the 2005 international conference on Comparative Genomics
Efficient sampling of transpositions and inverted transpositions for bayesian MCMC
WABI'06 Proceedings of the 6th international conference on Algorithms in Bioinformatics
Alignment with non-overlapping inversions in O(n3)-time
WABI'06 Proceedings of the 6th international conference on Algorithms in Bioinformatics
The approximability of the exemplar breakpoint distance problem
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
On the repeat-annotated phylogenetic tree reconstruction problem
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
A 2-approximation algorithm for sorting by prefix reversals
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Matrix tightness: a linear-algebraic framework for sorting by transpositions
SPIRE'06 Proceedings of the 13th international conference on String Processing and Information Retrieval
Genome rearrangements with partially ordered chromosomes
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Faster algorithms for sorting by transpositions and sorting by block-interchanges
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Lower bounds on the approximation of the exemplar conserved interval distance problem of genomes
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
The streaming complexity of cycle counting, sorting by reversals, and other problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The median problem for the reversal distance in circular bacterial genomes
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Approximating reversal distance for strings with bounded number of duplicates
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
A 1.375-approximation algorithm for sorting by transpositions
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
Minimum common string partition problem: hardness and approximations
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Partial enumeration of solutions traces for the problem of sorting by signed reversals
Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine
Inferring gene orders from gene maps using the breakpoint distance
RCG'06 Proceedings of the RECOMB 2006 international conference on Comparative Genomics
Evolution of tandemly repeated sequences through duplication and inversion
RCG'06 Proceedings of the RECOMB 2006 international conference on Comparative Genomics
A PQ framework for reconstructions of common ancestors and phylogeny
RCG'06 Proceedings of the RECOMB 2006 international conference on Comparative Genomics
Reversal distance for strings with duplicates: linear time approximation using hitting set
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
The 1.375 approximation algorithm for sorting by transpositions can run in O(n log n) time
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Conservation of combinatorial structures in evolution scenarios
RCG'04 Proceedings of the 2004 RECOMB international conference on Comparative Genomics
Genome rearrangement in mitochondria and its computational biology
RCG'04 Proceedings of the 2004 RECOMB international conference on Comparative Genomics
The distribution of inversion lengths in bacteria
RCG'04 Proceedings of the 2004 RECOMB international conference on Comparative Genomics
Sorting by weighted reversals, transpositions, and inverted transpositions
RECOMB'06 Proceedings of the 10th annual international conference on Research in Computational Molecular Biology
Sorting genomes using almost-symmetric inversions
Proceedings of the 27th Annual ACM Symposium on Applied Computing
Evolution of genome organization by duplication and loss: an alignment approach
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
Inapproximability of (1,2)-exemplar distance
ISBRA'12 Proceedings of the 8th international conference on Bioinformatics Research and Applications
Pivots, determinants, and perfect matchings of graphs
Theoretical Computer Science
Non-breaking similarity of genomes with gene repetitions
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
DCJ-indel distance with distinct operation costs
WABI'12 Proceedings of the 12th international conference on Algorithms in Bioinformatics
The distribution of cycles in breakpoint graphs of signed permutations
Discrete Applied Mathematics
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
Heuristics for the Sorting by Length-Weighted Inversion Problem
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
Sorting genomes by generalized translocations
Theoretical Computer Science
Inapproximability of (1,2)-Exemplar Distance
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Genomes frequently evolve by reversals &rgr;(i,j) that transform a gene order &pgr;1 … &pgr;i&pgr;i+1 … &pgr;j-1&pgr;j … &pgr;n into &pgr;1 … &pgr;i&pgr;j-1 … &pgr;i+1&pgr;j … &pgr;n. Reversal distance between permutations &pgr; and &sgr;is the minimum number of reversals to transform &pgr; into &Agr;. Analysis of genome rearrangements in molecular biology started in the late 1930's, when Dobzhansky and Sturtevant published a milestone paper presenting a rearrangement scenario with 17 inversions between the species of Drosophilia. Analysis of genomes evolving by inversions leads to a combinatorial problem of sorting by reversals studied in detail recently. We study sorting of signed permutations by reversals, a problem that adequately models rearrangements in a small genomes like chloroplast or mitochondrial DNA. 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 data. We prove a duality theorem explaining this intriguing performance and show that there exists a “hidden” parameter that allows one to compute the reversal distance between signed permutations in polynomial time.