Average-Case Analysis of Perfect Sorting by Reversals [chapter]

Mathilde Bouvel, Cedric Chauve, Marni Mishna, Dominique Rossin
2009 Lecture Notes in Computer Science  
Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any common interval. Bérard et al. (2007) make use of strong interval trees to describe an algorithm for sorting signed permutations by reversals. Combinatorial properties of this family of trees are essential to the algorithm analysis. Here, we use the expected
more » ... lue of certain tree parameters to prove that the average run-time of the algorithm is at worst, polynomial, and additionally, for sufficiently long permutations, the sorting algorithm runs in polynomial time with probability one. Furthermore, our analysis of the subclass of commuting scenarios yields precise results on the average length of a reversal, and the average number of reversals.
doi:10.1007/978-3-642-02441-2_28 fatcat:rrkj5qxu5fhqzkmhq3jxxwklpq