2012/01/04 by Mathilde Bouvel, Cédric Chauve, Bouvel, Mathilde +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #05A05 #05A16 #05C05 #05C90 #Algorithms and Data Compression #Combinatorics (math.CO) #DNA and Biological Computing #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Genome Rearrangement Algorithms #Quantitative Methods (q-bio.QM)
paper · pdf · doi:10.48550/arxiv.1201.0940
openalex publication_date 2012/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.