Sorting by Weighted Reversals and Transpositions

Genome rearrangements are global mutations that change large stretches of DNA sequence throughout genomes. They are rare but accumulate during the evolutionary process leading to organisms with similar genetic material in different places and orientations within the genome. Sorting by Genome Rearrangements problems seek for minimum-length sequences of rearrangements that transform one genome into the other. These problems accept alternative versions that assign weights for each event and the goal is to find a minimum-weight sequence. We study the Sorting by Weighted Reversals and Transpositions problem in two variants depending on whether we model genomes as signed or unsigned permutations. Here, we use weight 2 for reversals and 3 for transpositions and consider theoretical and practical aspects in our analysis. We present one algorithm with an approximation factor of 2 for both signed or unsigned permutations, and one algorithm with an approximation factor of 5/3 for signed permutations. We also analyze the behavior of the 5/3-approximation algorithm with different weights for reversals and transpositions.