Parallel Algorithm to Enumerate Sorting Reversals for Signed Permutation

The arrangement distance between singlechromosome genomes can be estimated as the minimum number of inversions required to transform the gene ordering observed in one into that observed in the other. This measure, known as “inversion distance,” can be computed as the reversal distance between signed permutations. During the past decade, much progress has been made both on the problem of computing reversal distance and on the related problem of finding a minimum-length sequence of reversals, which is known as “sorting by reversals.” In comparative genomics, algorithms that sort permutations by reversals are often used to propose evolutionary scenarios of large-scale genomic mutations between species. One of the main problems of such methods is that they give one solution while the number of optimal solutions is huge, with no criteria to discriminate among them. Bergeron et al. started to give some structure to the set of optimal solutions, in order to be able to deliver more presentable results than only one solution or a complete list of all solutions. This paper presents parallel algorithms to enumerate total sorting sequence of two signed permutations. These algorithms are based on Hannenhalli and Pevzner’s theory and composed of four key steps: Construct break point graph, compute the optimal distance, find the possible next reversal sequence and finally enumerate the total possible sorting sequences.