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.
Most proofs are omitted in this extended abstract. The full version with complete proofs is available at ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/ 2001/TR01-047.
Research done in part while visiting Dept. of Computer Science, University of Bonn. Work partially supported by NSF grant CCR-9700053, NIH grant 9R01HG02238-12 and DFG grant Bo 56/157-1.
Research done in part while vising Dept. of Computer Science, Princeton University. Work partially supported by DFG grants, DIMACS, and IST grant 14036 (RAND-APX).
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References
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.
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.
P. Berman and M. Fürer, Approximating independent set problem in bounded degree graphs, Proc. SODA 1994, 365–371.
P. Berman and S. Hannenhalli, Fast Sorting by Reversals, Proc. of 7th CPM, 168–185, 1996.
P. Berman and M. Karpinski, On some tighter inapproximability results, Proc. of 26th ICALP, LNCS 1644:200–209, Springer-Verlag, Berlin, 1999.
A. Caprara, Sorting by Reversals is difficult, Proc. of 1st ACM RECOMB, 75–83, 1997, to appear in SIAM J. of Discr. Math. 2001.
D.A. Christie, A 3/2 Approximation algorithm for sorting by reversals, Proc. of 9th ACM-SIAM SODA, 244–252, 1998.
D. Cohen and M. Blum, On the problem of Sorting Burnt Pancakes, Discrete Appl. Math. 61:105–125, 1995.
W.H. Gates and C.H. Papadimitriou, Bounds for sorting by pre.x reversals, Discr. Math. 27:47–57, 1979.
M. M. Halldórsson and K. Yoshikara, Greedy approximation of independent sets in low degree graphs
S. Hannenhalli and P. Pevzner, Transforming cabbage into turnip, Proc. of 27th ACM STOC 1995, 178–189.
S. Hannenhalli and P. Pevzner, To cut... or not to cut, Proc. of 7th ACMSIAM SODA 1996, 304–313.
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.
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.
J. Kececioglu and D. Sanko., Exact and approximation algorithms for the inversion distance between two permutations, Algorithmica 13:180–210, 1995.
P. Pevzner, Computational Molecular Biology-An Algorithmic Approach, The MIT Press, Cambridge, 2000.
D. Sanko., 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.
D. Sanko., 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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Berman, P., Hannenhalli, S., Karpinski, M. (2002). 1.375-Approximation Algorithm for Sorting by Reversals. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_21
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DOI: https://doi.org/10.1007/3-540-45749-6_21
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