Article

1.375-Approximation Algorithm for Sorting by Reversals

Authors:

Sridhar Hannenhalli,

Marek KarpinskiAuthors Info & Claims

ESA '02: Proceedings of the 10th Annual European Symposium on Algorithms

Pages 200 - 210

Published: 17 September 2002 Publication History

Abstract

Analysis of genomes evolving by inversions leads to a general combinatorial problem of Sorting by Reversals, MIN-SBR, the problem of sorting a permutation by a minimum number of reversals. Following a series of preliminary results, Hannenhalli and Pevzner developed the first exact polynomial time algorithm for the problem of sorting signed permutations by reversals, and a polynomial time algorithm for a special case of unsigned permutations. The best known approximation algorithm for MIN-SBR, due to Christie, gives a performance ratio of 1.5. In this paper, by exploiting the polynomial time algorithm for sorting signed permutations and by developing a new approximation algorithm for maximum cycle decomposition of breakpoint graphs, we design a new 1.375-algorithm for the MIN-SBR problem.

References

[1]

N. Amato, M. Blum, S. Irani and R. Rubinfeld, Reversing Trains: a turn of the century sorting problem , J. of Algorithms 10 :413-428, 1989.

[2]

V. Bafna and P. Pevzner, Genome rearrangements and sorting by reversals , Proc. of 34th IEEE FOCS, 148-157, 1993; also in SIAM J. on Computing 25 :272-289, 1996.

[3]

P. Berman and M. Fürer, Approximating independent set problem in bounded degree graphs , Proc. SODA 1994, 365-371.

[4]

P. Berman and S. Hannenhalli, Fast Sorting by Reversals , Proc. of 7th CPM, 168-185, 1996.

[5]

P. Berman and M. Karpinski, On some tighter inapproximability results , Proc. of 26th ICALP, LNCS 1644 :200-209, Springer-Verlag, Berlin, 1999.

[6]

A. Caprara, Sorting by Reversals is difficult , Proc. of 1st ACM RECOMB, 75-83, 1997, to appear in SIAM J. of Discr. Math. 2001.

[7]

D.A. Christie, A 3/2 Approximation algorithm for sorting by reversals , Proc. of 9th ACM-SIAM SODA, 244-252, 1998.

[8]

D. Cohen and M. Blum, On the problem of Sorting Burnt Pancakes , Discrete Appl. Math. 61 :105-125, 1995.

[9]

W. H. Gates and C. H. Papadimitriou, Bounds for sorting by prefix reversals , Discr. Math. 27 :47-57, 1979.

[10]

M. M. Halldórsson and K. Yoshikara, Greedy approximation of independent sets in low degree graphs .

[11]

S. Hannenhalli and P. Pevzner, Transforming cabbage into turnip , Proc. of 27th ACM STOC 1995, 178-189.

[12]

S. Hannenhalli and P. Pevzner, To cut... or not to cut , Proc. of 7th ACM-SIAM SODA 1996, 304-313.

[13]

C. A. J. Hurkens and A. Schcrijver, On the size of systems of sets every t of which have an SDR, with an aplication to the worst case ratio of heuristic for Packing Problem , SIAM J. of Discr. Math. 2 (1):62-72, 1989.

[14]

H. Kaplan, R. Shamir and R.E. Tarjan, Faster and simpler algorithm for sorting signed permutations by reversals , Proc. of 8th ACM-SIAM SODA, 178-187, 1997.

[15]

J. Kececioglu and D. Sankoff, Exact and approximation algorithms for the inversion distance between two permutations , Algorithmica 13 :180-210, 1995.

[16]

P. Pevzner, Computational Molecular Biology--An Algorithmic Approach , The MIT Press, Cambridge, 2000.

[17]

D. Sankoff, R. Cedergen and Y. Abel, Genomic divergence through gene rearrangement , in Molecular Evolution: Computer Analysis of Protein and Nucleic Acid Sequences , chapter 26, 428-238, Academic Press, 1990.

[18]

D. Sankoff, G. Leduc, N. Antoine, B. Paquin, B. F. Lang and R. Cedergen, Gene order comparisons for phylogenetic inference: Evolution of the mitochondrial genome , Proc. Natl. Acad. Sci. USA, 89 :6575-6579, 1992.

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cover image Guide Proceedings

ESA '02: Proceedings of the 10th Annual European Symposium on Algorithms

September 2002

925 pages

ISBN:3540441808

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 17 September 2002

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Cited By

Baioletti MMilani ASantucci VBartoccini UAuger AStützle T(2019)An experimental comparison of algebraic differential evolution using different generating setsProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3319619.3326854(1527-1534)Online publication date: 13-Jul-2019
https://dl.acm.org/doi/10.1145/3319619.3326854
Zhai SZhang PZhu DTong WXu YLin G(2019)An approximation algorithm for genome sorting by reversals to recover all adjacenciesJournal of Combinatorial Optimization10.1007/s10878-018-0346-y37:4(1170-1190)Online publication date: 1-May-2019
https://dl.acm.org/doi/10.1007/s10878-018-0346-y
Seo JKim JChang HLee H(2018)The hierarchical Petersen networkThe Journal of Supercomputing10.1007/s11227-017-2186-474:4(1636-1654)Online publication date: 1-Apr-2018
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Bulteau LFertin GKomusiewicz C(2016)(Prefix) reversal distance for (signed) strings with few blocks or small alphabetsJournal of Discrete Algorithms10.1016/j.jda.2016.05.00237:C(44-55)Online publication date: 1-Mar-2016
https://dl.acm.org/doi/10.1016/j.jda.2016.05.002
Chatterjee KChmelík MTracol M(2016)What is decidable about partially observable Markov decision processes with ω-regular objectivesJournal of Computer and System Sciences10.1016/j.jcss.2016.02.00982:5(878-911)Online publication date: 1-Aug-2016
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Soncco-Álvarez JAlmeida GBecker JAyala-Rincón M(2015)Parallelization of genetic algorithms for sorting permutations by reversals over biological dataInternational Journal of Hybrid Intelligent Systems10.3233/HIS-14020512:1(53-64)Online publication date: 1-Jan-2015
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Galvão GDias Z(2015)An Audit Tool for Genome Rearrangement AlgorithmsACM Journal of Experimental Algorithmics10.1145/266163319(1.1-1.34)Online publication date: 7-Jan-2015
https://dl.acm.org/doi/10.1145/2661633
Lintzmayer CFertin GDias Z(2015)Approximation algorithms for sorting by length-weighted prefix and suffix operationsTheoretical Computer Science10.1016/j.tcs.2015.05.039593:C(26-41)Online publication date: 16-Aug-2015
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Jiang HWang LZhu BZhu D(2015)A factor-(1.408+ε) approximation for sorting unsigned genomes by reciprocal translocationsTheoretical Computer Science10.1016/j.tcs.2015.04.036607:P2(166-180)Online publication date: 23-Nov-2015
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Bulteau LFertin GRusu I(2015)Pancake Flipping is hardJournal of Computer and System Sciences10.1016/j.jcss.2015.02.00381:8(1556-1574)Online publication date: 1-Dec-2015
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