2014/10/09 by Katharine Adamyk, Adamyk, K. L. M., Erik Holmes +11 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #05A05 #05E15 #20B99 #68P10 #91A46 #92-08 #92D15 #97A20 #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics #Genome Rearrangement Algorithms #Genomics and Phylogenetic Studies
paper · pdf · doi:10.48550/arxiv.1410.2353
openalex publication_date 2014/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Permutation sorting, one of the fundamental steps in pre-processing data for the efficient application of other algorithms, has a long history in mathematical research literature and has numerous applications. Two special-purpose sorting operations are considered in this paper: context directed swap, abbreviated cds, and context directed reversal, abbreviated cdr. These are special cases of sorting operations that were studied in prior work on permutation sorting. Moreover, cds and cdr have been postulated to model molecular sorting events that occur in the genome maintenance program of certain species of single-celled organisms called ciliates. This paper investigates mathematical aspects of these two sorting operations. The main result of this paper is a generalization of previously discovered characterizations of cds-sortability of a permutation. The combinatorial structure underlying this generalization suggests natural combinatorial two-player games. These games are the main mathematical innovation of this paper.