Prefix transpositions on binary and ternary strings

Prefix and suffix transreversals on binary and ternary strings

“…Therefore, the equivalence relation here is that if we remove the adjacent identical symbols, all strings of a class reduce to the same normalized string (i.e., the representative of the class). We remark that the concepts of normalization, reduction and equivalence class have been borrowed from the previous works of [3,5]. Now, we provide an example demonstrating the scenario of performing the rearrangement operations on a binary string.…”

“…We follow the notations and definitions used in [3] and [5], which are briefly reviewed below for the sake of completeness. We use [k] to denote the first k non-negative integers {0, 1, .…”

“…This shift is inspired by the biological observation that multiple "copies" of the same gene can appear at various places along the genome [3,5]. Indeed, recent works by Christie and Irving [2], Dutta et al [3], Radcliffe et al [7] and Hurkens et al [5] explore the consequences of switching from permutations to strings. Notably, such rearrangement operations on strings have been found to be interesting and important in the study of orthologous gene assignment [1], especially if the strings have only low level of symbol repetition.…”

“…In the sequel, they gave a complete characterization of the minimum number of prefix reversals required to group (and sort) binary and ternary strings. Finally, Dutta, Hasan and Rahman [3] followed up the work of [5], and considered prefix transpositions introducing a relabeling technique. In particular, they gave a complete characterization of the minimum number of prefix transpositions required to group (and sort) binary and ternary strings.…”

“…In this paper, we follow up the work of [3,5] and motivated by [6], consider prefix and suffix transreversals to group and sort binary and ternary strings. Notably, as a future work in [5], the authors raised the issue of considering other genome arrangement operators.…”