Merging and Sorting By Strip Moves

We consider two problems related to the well-studied sorting by transpositions problem: (1) Given a permutation, sort it by moving a minimum number of strips, where a strip is a maximal substring of the permutation which is also a substring of the identity permutation, and (2) Given a set of increasing sequences of distinct elements, merge them into one increasing sequence with a minimum number of strip moves. We show that the merging by strip moves problem has a polynomial time algorithm. Using this, we give a 2-approximation algorithm for the sorting by strip moves problem. We also observe that the sorting by strip moves problem, as well as the sorting by transpositions problem, are fixed-parameter-tractable.

[1]  Michael R. Fellows,et al.  DNA Physical Mapping: Three Ways Difficult , 1993, ESA.

[2]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .

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

[4]  David A. Christie,et al.  Sorting Permutations by Block-Interchanges , 1996, Inf. Process. Lett..

[5]  David Sankoff,et al.  Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement , 1995, Algorithmica.

[6]  Niklas Eriksen,et al.  (1+epsilon)-Approximation of sorting by reversals and transpositions , 2001, Theor. Comput. Sci..

[7]  S Heath Lenwood,et al.  Sorting by Short Block-Moves , 1998 .

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

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

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

[11]  Michael R. Fellows,et al.  Parameterized complexity analysis in computational biology , 1995, Comput. Appl. Biosci..

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

[13]  Robert W. Irving,et al.  Sorting Strings by Reversals and by Transpositions , 2001, SIAM J. Discret. Math..

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

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