Extending Bafna-Pevzner algorithm

Genome Rearrangement is a field that addresses the problem of finding the minimum number of global operations, such as transpositions, reversals, fusions and fissions that transform a given genome into another. In this work we deal with transposition events, which are events that change the position of two contiguous block of genes in the same chromosome. Some approximation algorithms for this problem were published so far. Bafna and Pevzner [1] proposed the first 1.5-approximation algorithm for the transposition distance problem and recently Elias and Hartman [4] delineated a 1.375-approximation algorithm, which is currently the best performance ratio known. Many other algorithms achieve good performance on experimental results and provide new insights to solve the problem [2, 5, 8, 9, 11]. In this paper we present two main results. The first result is the implementation of the 1.375-algorithm described by Elias and Hartman [4]. We also compared the experimental results from Elias-Hartman algorithm with other approaches. It is important to realize that no implementation of Elias-Hartman algorithm was provided before this work and the approximation proof was assisted by a computer program. Although the approximation ratio is an important issue, we need to know how the algorithm behaves on practical experiments. For this reason, we show the experimental results of Elias-Hartman algorithm using our datasets. The second result is the description of our algorithm based on Bafna and Pevzner [1] 1.5-approximation algorithm. Our algorithm uses a set of heuristics that allowed us to improve the solution quality of the original algorithm, but keeping the original 1.5-approximation ratio. We compare our experimental results with the best results published so far. The results indicate that our algorithm performs best in practice. The solution quality analysis also shows that our algorithm outperforms Elias and Hartman 1.375-approximation algorithm on longer permutations, despite the approximation ratio. We delineate an algorithm for the transposition distance problem. Our algorithm is the first polynomial time algorithm that sorts by transposition any permutation π, for |π| = 9. We show that our algorithm is better than the other algorithms using sequences π, for π < 11. We also show that our algorithm keeps the good performance on longer permutations. We claim that the heuristics proposed in this work contribute for discovering the complexity of sorting by transposition, which remains open.