On Sorting under Special Transpositions

In this paper, we study a genome rearrangement primitive called block moves. This primitive as a special case of another well studied primitive transposition. We revisit the problem of BLOCK SORTING, which is a sorting problem under the primitive block moves in this work. BLOCK SORTING has been shown to be NP-Complete, and a couple of results have designed factor 2 approximation algorithms for the problem - the best known till date. However whether the problem is APX-Hard, or an improvement over the factor 2 approximation algorithms have been interesting open problems. We design a new factor 2 approximation algorithm for BLOCK SORTING. Our algorithm is equal to the best known in terms of approximation ratio, however, our approach is much simpler and is linear time (O (n)) as compared to the cubic (O (n³)) and quadratic (O (n²)) run-times of the existing algorithms for the problem.