An O(n3/2sqrt(log(n))) algorithm for sorting by reciprocal translocations

We prove that sorting by reciprocal translocations can be done in O(n 3/2 √log(n)) for an n-gene genome. Our algorithm is an adaptation of the Tannier et. al algorithm for sorting by reversals. This improves over the O(n 3 ) algorithm for sorting by reciprocal translocations given by Bergeron et al.

[1]  Jens Stoye,et al.  Reversal Distance without Hurdles and Fortresses , 2004, CPM.

[2]  Anne Bergeron A very elementary presentation of the Hannenhalli-Pevzner theory , 2005, Discret. Appl. Math..

[3]  Ron Shamir,et al.  An O(n3/2sqrt(log n)) Algorithm for Sorting by Reciprocal Translocations , 2006, CPM.

[4]  Lusheng Wang,et al.  An O(N2) algorithm for signed translocation problem , 2005, APBC.

[5]  Pavel A. Pevzner,et al.  Transforming Cabbage into Turnip: Polynomial Algorithm for Sorting Signed Permutations by Reversals , 1999, J. ACM.

[6]  Haim Kaplan,et al.  A Faster and Simpler Algorithm for Sorting Signed Permutations by Reversals , 1999, SIAM J. Comput..

[7]  Binhai Zhu,et al.  A Linear-Time Algorithm for Computing Translocation Distance between Signed Genomes , 2004, CPM.

[8]  Lusheng Wang,et al.  An O(n2) algorithm for signed translocation , 2005, J. Comput. Syst. Sci..

[9]  Pavel A. Pevzner,et al.  Transforming men into mice (polynomial algorithm for genomic distance problem) , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[10]  Haim Kaplan,et al.  Sorting signed permutations by reversals, revisited , 2005, J. Comput. Syst. Sci..

[11]  Anne Bergeron,et al.  Advances on sorting by reversals , 2007, Discret. Appl. Math..

[12]  Ron Shamir,et al.  Sorting by Reciprocal Translocations via Reversals Theory , 2007, J. Comput. Biol..

[13]  Sridhar Hannenhalli,et al.  Polynomial-time Algorithm for Computing Translocation Distance Between Genomes , 1995, Discret. Appl. Math..

[14]  Ron Shamir,et al.  Sorting by Translocations Via Reversals Theory , 2006, Comparative Genomics.

[15]  David A. Bader,et al.  A Linear-Time Algorithm for Computing Inversion Distance between Signed Permutations with an Experimental Study , 2001, J. Comput. Biol..

[16]  Jens Stoye,et al.  On Sorting by Translocations , 2006, J. Comput. Biol..

[17]  R. Ravi,et al.  Of mice and men: algorithms for evolutionary distances between genomes with translocation , 1995, SODA '95.

[18]  Piotr Berman,et al.  Fast Sorting by Reversal , 1996, CPM.