A 1.375-Approximation Algorithm for Sorting by Transpositions

Sorting permutations by transpositions is an important problem in genome rearrangements. A transposition is a rearrangement operation in which a segment is cut out of the permutation and pasted in a different location. The complexity of this problem is still open and it has been a 10-year-old open problem to improve the best known 1.5-approximation algorithm. In this paper, we provide a 1.375-approximation algorithm for sorting by transpositions. The algorithm is based on a new upper bound on the diameter of 3-permutations. In addition, we present some new results regarding the transposition diameter: We improve the lower bound for the transposition diameter of the symmetric group and determine the exact transposition diameter of simple permutations

[1]  Carito Guziolowski,et al.  Algorithms for Molecular Biology , 2007 .

[2]  David Alan Christie,et al.  Genome rearrangement problems , 1998 .

[3]  J. Palmer,et al.  Tricircular mitochondrial genomes of Brassica and Raphanus: reversal of repeat configurations by inversion. , 1986, Nucleic acids research.

[4]  Rick Durrett,et al.  Genome rearrangement , 2022 .

[5]  Henrik Eriksson,et al.  Sorting a bridge hand , 2001, Discret. Math..

[6]  Vineet Bafna,et al.  Genome Rearrangements and Sorting by Reversals , 1996, SIAM J. Comput..

[7]  P.A. Pevzner,et al.  Open combinatorial problems in computational molecular biology , 1995, Proceedings Third Israel Symposium on the Theory of Computing and Systems.

[8]  Tzvika Hartman,et al.  A 1.375-Approximation Algorithm for Sorting by Transpositions , 2005, WABI.

[9]  Pavel A. Pevzner,et al.  Computational molecular biology : an algorithmic approach , 2000 .

[10]  Guohui Lin,et al.  Signed genome rearrangement by reversals and transpositions: models and approximations , 2001, Theor. Comput. Sci..

[11]  Shietung Peng,et al.  A 2-Approximation Algorithm for Genome Rearrangements by Reversals and Transpositions , 1999, Theor. Comput. Sci..

[12]  Marek Karpinski,et al.  1.375-Approximation Algorithm for Sorting by Reversals , 2002, ESA.

[13]  K. Appel,et al.  Every planar map is four colorable. Part I: Discharging , 1977 .

[14]  Guohui Lin,et al.  Signed Genome Rearrangement by Reversals and Transpositions: Models and Approximations , 1999, COCOON.

[15]  Pavel A. Pevzner,et al.  Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals , 1995, JACM.

[16]  Marie-France Sagot,et al.  Sorting by Reversals in Subquadratic Time , 2004, CPM.

[17]  Vineet Bafna,et al.  Genome rearrangements and sorting by reversals , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

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

[19]  Uri Zwick,et al.  Computer assisted proof of optimal approximability results , 2002, SODA '02.

[20]  Jeffrey D. Palmer,et al.  Structural rearrangements, including parallel inversions, within the chloroplast genome of Anemone and related genera , 1994, Journal of Molecular Evolution.

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

[22]  Roded Sharan,et al.  A 1.5-approximation algorithm for sorting by transpositions and transreversals , 2004, J. Comput. Syst. Sci..

[23]  Alberto Caprara,et al.  Sorting Permutations by Reversals and Eulerian Cycle Decompositions , 1999, SIAM J. Discret. Math..

[24]  Tzvika Hartman,et al.  A Simpler 1.5-Approximation Algorithm for Sorting by Transpositions , 2003, CPM.

[25]  Ron Shamir,et al.  A simpler and faster 1.5-approximation algorithm for sorting by transpositions , 2006, Inf. Comput..

[26]  Vineet Bafna,et al.  Sorting by Transpositions , 1998, SIAM J. Discret. Math..

[27]  Haim Kaplan,et al.  Faster and simpler algorithm for sorting signed permutations by reversals , 1997, SODA '97.

[28]  R. Gentleman.  Current Topics in Computational Molecular Biology , 2004 .

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