AVERAGE-CASE ANALYSIS OF PERFECT SORTING BY REVERSALS

作     者：Bouvel, Mathilde Chauve, Cedric Mishna, Marni Rossin, Dominique 

作者机构：Univ Bordeaux 1 CNRS LaBRI Bordeaux France Simon Fraser Univ Dept Math Burnaby BC V5A 1S6 Canada Ecole Polytech CNRS LIX Palaiseau France 

出 版 物：《DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS》 (Discret. Math. Algorithms Appli.)

年 卷 期：2011年第3卷第3期

页      面：369-392页

基　　金：Discovery Grant program of the Natural Science and Engineering Research Council (Canada) ANR projects GAMMA [BLAN-072195422] MAGNUM [2010_BLAN_0204] 

主　　题：Algorithm analysis genome rearrangements tree parameters simple permutations 

摘      要：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. Berard 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 value 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.