Sorting by reversals is difficult
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
Formulations and hardness of multiple sorting by reversals
RECOMB '99 Proceedings of the third annual international conference on Computational molecular biology
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
The complexity of gene placement
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A 3/2-approximation algorithm for sorting by reversals
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Fast practical solution of sorting by reversals
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Gossip is synteny: incomplete gossip and an exact algorithm for syntenic distance
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Gossip is synteny: incomplete gossip and the syntenic distance between genomes
Journal of Algorithms
Packing triangles in bounded degree graphs
Information Processing Letters
Transforming men into mice: the Nadeau-Taylor chromosomal breakage model revisited
RECOMB '03 Proceedings of the seventh annual international conference on Research in computational molecular biology
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
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
On Some Tighter Inapproximability Results (Extended Abstract)
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Sorting by Prefix Transpositions
SPIRE 2002 Proceedings of the 9th International Symposium on String Processing and Information Retrieval
Structural Properties and Tractability Results for Linear Synteny
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
Packing Cycles and Cuts in Undirected Graphs
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
1.375-Approximation Algorithm for Sorting by Reversals
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Approximating Bounded Degree Instances of NP-Hard Problems
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
A new approximation algorithm for sorting of signed permutations
Journal of Computer Science and Technology
Improved bounds on sorting with length-weighted reversals
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Integer programming models for computational biology problems
Journal of Computer Science and Technology - Special issue on bioinformatics
Packing cycles in undirected graphs
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
On maximal instances for the original syntenic distance
Theoretical Computer Science
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
A simpler and faster 1.5-approximation algorithm for sorting by transpositions
Information and Computation
On the complexity of unsigned translocation distance
Theoretical Computer Science
A 1.375-Approximation Algorithm for Sorting by Transpositions
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
Faster algorithms for sorting by transpositions and sorting by block interchanges
ACM Transactions on Algorithms (TALG)
A 1.75-approximation algorithm for unsigned translocation distance
Journal of Computer and System Sciences
Whole genome duplications, multi-break rearrangements, and genome halving problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Reconstruction of permutations distorted by reversal errors
Discrete Applied Mathematics
Improved bounds on sorting by length-weighted reversals
Journal of Computer and System Sciences
Multi-break rearrangements and chromosomal evolution
Theoretical Computer Science
An approximation algorithm for sorting by reversals and transpositions
Journal of Discrete Algorithms
On the Toric Graph as a Tool to Handle the Problem of Sorting by Transpositions
BSB '08 Proceedings of the 3rd Brazilian symposium on Bioinformatics: Advances in Bioinformatics and Computational Biology
On Computing the Breakpoint Reuse Rate in Rearrangement Scenarios
RECOMB-CG '08 Proceedings of the international workshop on Comparative Genomics
Internal Validation of Ancestral Gene Order Reconstruction in Angiosperm Phylogeny
RECOMB-CG '08 Proceedings of the international workshop on Comparative Genomics
A quadratic time 2-approximation algorithm for block sorting
Theoretical Computer Science
Block sorting: a characterization and some heuristics
Nordic Journal of Computing
On approximating four covering and packing problems
Journal of Computer and System Sciences
Hardness and approximation of traffic grooming
Theoretical Computer Science
RECOMB-CG '09 Proceedings of the International Workshop on Comparative Genomics
A simpler and faster 1.5-approximation algorithm for sorting by transpositions
Information and Computation
A simpler 1.5-approximation algorithm for sorting by transpositions
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
Efficient data structures and a new randomized approach for sorting signed permutations by reversals
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
Signed genome rearrangement by reversals and transpositions: models and approximations
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Multi-break rearrangements: from circular to linear genomes
RECOMB-CG'07 Proceedings of the 2007 international conference on Comparative genomics
How to achieve an equivalent simple permutation in linear time
RECOMB-CG'07 Proceedings of the 2007 international conference on Comparative genomics
O(1)-time unsorting by prefix-reversals in a boustrophedon linked list
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
On sorting permutations by double-cut-and-joins
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
The transposition median problem is NP-complete
Theoretical Computer Science
Sorting unsigned permutations by weighted reversals, transpositions, and transreversals
Journal of Computer Science and Technology
Unitary Toric Classes, the Reality and Desire Diagram, and Sorting by Transpositions
SIAM Journal on Discrete Mathematics
Computing rearrangement distance of every permutation in the symmetric group
Proceedings of the 2011 ACM Symposium on Applied Computing
Weighted genomic distance can hardly impose a bound on the proportion of transpositions
RECOMB'11 Proceedings of the 15th Annual international conference on Research in computational molecular biology
A Lower Bound on the Transposition Diameter
SIAM Journal on Discrete Mathematics
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
A 1.75-approximation algorithm for unsigned translocation distance
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
A 1.375-approximation algorithm for sorting by transpositions
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
A faster and simpler 2-approximation algorithm for block sorting
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Genome halving problem revisited
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
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
A simplified view of DCJ-indel distance
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
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Sequence comparison in molecular biology is in the beginning of a major paradigm shift---a shift from gene comparison based on local mutations (i.e., insertions, deletions, and substitutions of nucleotides) to chromosome comparison based on global rearrangements (i.e., inversions and transpositions of fragments). The classical methods of sequence comparison do not work for global rearrangements, and little is known in computer science about the edit distance between sequences if global rearrangements are allowed. In the simplest form, the problem of gene rearrangements corresponds to sorting by reversals, i.e., sorting of an array using reversals of arbitrary fragments. Recently, Kececioglu and Sankoff gave the first approximation algorithm for sorting by reversals with guaranteed error bound 2 and identified open problems related to chromosome rearrangements. One of these problems is Gollan's conjecture on the reversal diameter of the symmetric group. This paper proves the conjecture. Further, the problem of expected reversal distance between two random permutations is investigated. The reversal distance between two random permutations is shown to be very close to the reversal diameter, thereby indicating that reversal distance provides a good separation between related and nonrelated sequences in molecular evolution studies. The gene rearrangement problem forces us to consider reversals of signed permutations, as the genes in DNA could be positively or negatively oriented. An approximation algorithm for signed permutation is presented, which provides a performance guarantee of ${3 \over 2}$. Finally, using the signed permutations approach, an approximation algorithm for sorting by reversals is described which achieves a performance guarantee of ${7 \over 4}$.