Multiple genome rearrangement by reversals

In this paper, we discuss a multiple genome rearrangement problem: Given a collection of genomes represented by permutations, we generate the collection from some fixed genome, e.g., the identity permutation, in a minimum number of signed reversals. It is NP-hard, so efficient heuristics is important for finding its optimal solution. We at first discuss how to generate two and three genomes from a fixed genome by polynomial algorithms for some special cases. Then based on the polynomial algorithms, we obtain some approximation algorithms for generating two and three genomes in general, respectively. Finally, we apply these approximation algorithms to design a new approximation algorithm for generating more genomes. We also show by some experimental examples that the algorithms are efficient.