Sorting permutations by prefix and suffix rearrangements

作者：Lintzmayer Carla Negri; Fertin Guillaume; Dias Zanoni

来源：Journal of Bioinformatics and Computational Biology, 2017, 15(1): 1750002.

DOI：10.1142/S0219720017500020

• Permutations
• sorting
• reversals
• transpositions
• prefix
• suffix
• approximation algorithms
• diameter

Some interesting combinatorial problems have been motivated by genome rearrangements, which are mutations that affect large portions of a genome. When we represent genomes as permutations, the goal is to transform a given permutation into the identity permutation with the minimum number of rearrangements. When they affect segments from the beginning (respectively end) of the permutation, they are called prefix (respectively suffix) rearrangements. This paper presents results for rearrangement problems that involve prefix and suffix versions of reversals and transpositions considering unsigned and signed permutations. We give 2- approximation and (2 +lambda)-approximation algorithms for these problems, where lambda is a constant divided by the number of breakpoints (pairs of consecutive elements that should not be consecutive in the identity permutation) in the input permutation. We also give bounds for the diameters concerning these problems and provide ways of improving the practical results of our algorithms.

• 出版日期2017-2