SIAM Journal on Discrete Mathematics
A 2-approximation algorithm for genome rearrangements by reversals and transpositions
Theoretical Computer Science - Special issue: Genome informatics
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
A Faster and Simpler Algorithm for Sorting Signed Permutations by Reversals
SIAM Journal on Computing
An algorithm to enumerate all sorting reversals
Proceedings of the sixth annual international conference on Computational biology
A Very Elementary Presentation of the Hannenhalli-Pevzner Theory
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
1.375-Approximation Algorithm for Sorting by Reversals
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
(1+epsilon)-Approximation of Sorting by Reversals and Transpositions
WABI '01 Proceedings of the First International Workshop on Algorithms in Bioinformatics
ParIS Genome Rearrangement server
Bioinformatics
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
Genome rearrangement in mitochondria and its computational biology
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
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The evolutionary distance between two organisms can be determined by comparing the order of appearance of orthologous genes in their genomes. Above the numerous parsimony approaches that try to obtain the shortest sequence of rearrangement operations sorting one genome into the other, Bayesian Markov chain Monte Carlo methods have been introduced a few years ago. The computational time for convergence in the Markov chain is the product of the number of needed steps in the Markov chain and the computational time needed to perform one MCMC step. Therefore faster methods for making one MCMC step can reduce the mixing time of an MCMC in terms of computer running time. We introduce two efficient algorithms for characterizing and sampling transpositions and inverted transpositions for Bayesian MCMC. The first algorithm characterizes the transpositions and inverted transpositions by the number of breakpoints the mutations change in the breakpoint graph, the second algorithm characterizes the mutations by the change in the number of cycles. Both algorithms run in O(n) time, where n is the size of the genome. This is a significant improvement compared with the so far available brute force method with O(n3) running time and memory usage.