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Sorting by reversals

One of the most studied problems in the field of computational biology is the string matching problem. Much of the reasearch has focused on developing efficient algorithms for transforming one string into another by minimizing the number of steps. The biological motivation for this problem comes from the fact that DNA sequences get transformed by a series of basic operations such as mutations, deletions and substitutions. When trying to understand how genetic sequences mutate at the chromosome level we need to consider more global operations, rather than the basic ones. One of the most common global mutation is the reversing of a substring, operation also known as a reversal. In fact, the minimum number of reversals used to transform one string into another has proven to be a very good estimate for the evolutionary distance between organisms. The problem presented in this paper is finding the minimum number of reversals needed to transform one string into another. Two variants of this problem together with results taken from [1] and [2] are going to be presented in the following sections.