Sorting permutations by block-interchanges
Information Processing Letters
SIAM Journal on Discrete Mathematics
Sorting permutations by tanspositions
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Transforming men into mice (polynomial algorithm for genomic distance problem)
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
A New Approach for Approximating the Transposition Distance
SPIRE '00 Proceedings of the Seventh International Symposium on String Processing Information Retrieval (SPIRE'00)
A 1.375-approximation algorithm for sorting by transpositions
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
A new and faster method of sorting by transpositions
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Constraint Programming Models for Transposition Distance Problem
BSB '09 Proceedings of the 4th Brazilian Symposium on Bioinformatics: Advances in Bioinformatics and Computational Biology
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In computational biology, genome rearrangements is a field in which we study mutational events affecting large portions of a genome. One such event is the transposition, that changes the position of contiguous blocks of genes inside a chromosome. This event generates the problem of transposition distance, that is to find the minimal number of transpositions transforming one chromosome into another. It is not known whether this problem is $\mathcal{NP}$-hard or has a polynomial time algorithm. Some approximation algorithms have been proposed in the literature, whose proofs are based on exhaustive analysis of graphical properties of suitable cycle graphs. In this paper, we follow a different, more formal approach to the problem, and present a 1.5-approximation algorithm using an algebraic formalism. Besides showing the feasibility of the approach, the presented algorithm exhibits good results, as our experiments show.