Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Transforming men into mice (polynomial algorithm for genomic distance problem)
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
A very elementary presentation of the Hannenhalli-Pevzner theory
Discrete Applied Mathematics
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
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
Average-Case Analysis of Perfect Sorting by Reversals
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Listing all sorting reversals in quadratic time
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Listing all parsimonious reversal sequences: new algorithms and perspectives
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
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As data about genomic architecture accumulates, genomic rearrangements have attracted increasing attention. 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 characterization relies on the concepts of breakpoints, cycles, and obstructions colorfully named hurdles and fortresses. In this paper, we study the probability of generating a hurdle in the process of sorting a permutation if one does not take special precautions to avoid them (as in a randomized algorithm, for instance). To do this we revisit and extend the work of Caprara and of Bergeron by providing simple and exact characterizations of the probability of encountering a hurdle in a random permutation. Using similar methods we, for the first time, find an asymptotically tight analysis of the probability that a fortress exists in a random permutation.