WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Permutation Editing and Matching via Embeddings
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Edit Distance with Move Operations
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
On the Structure of Syntenic Distance
CPM '99 Proceedings of the 10th Annual Symposium on Combinatorial Pattern Matching
(1+epsilon)-Approximation of Sorting by Reversals and Transpositions
WABI '01 Proceedings of the First International Workshop on Algorithms in Bioinformatics
Sorting Genomes with Insertions, Deletions and Duplications by DCJ
RECOMB-CG '08 Proceedings of the international workshop on Comparative Genomics
On sorting permutations by double-cut-and-joins
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Polynomial-time sortable stacks of burnt pancakes
Theoretical Computer Science
Bounding prefix transposition distance for strings and permutations
Theoretical Computer Science
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Heuristics for the Sorting by Length-Weighted Inversion Problem
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
Topological morphing of planar graphs
Theoretical Computer Science
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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 to chromosome comparison based on global rearrangements. 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. Kececioglu and Sankoff gave the first approximation algorithm for sorting by reversals with guaranteed error bound and identified open problems related to chromosome rearrangements. One of these problems is Gollan's conjecture on the reversal diameter of the symmetric group. We prove this conjecture and further study the problem of expected reversal distance between two random permutations. We demonstrate that the expected reversal distance is very close to the reversal diameter thereby indicating that reversal distance provides a good separation between related and non-related sequences. The gene rearrangement problem forces us to consider reversals of signed permutations, as the genes in DNA are oriented. Our approximation algorithm for signed permutation provides a 'performance guarantee' of 3/2. Finally, we devise an approximation algorithm for sorting by reversals with a performance ratio of 7/4.