Sorting permutations by reversals and eulerian cycle decompositions

SIAM Journal on Discrete Mathematics

Volumn 12, Issue 1, 1999, Pages 91-110

  Caprara, Alberto ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Breakpoint graph; Complexity; Cycle decomposition; Eulerian graph; Sorting by reversals

Indexed keywords

EID: 0002721941     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S089548019731994X     Document Type: Article

References (21)

1. V. BAFNA AND P. A. PEVZNER, Genome rearrangements and sorting by reversals, SIAM J. Comput., 25 (1996), pp. 272-289.
2. P. BERMAN AND S. HANNENHALLI, Fast sorting by reversal, in Proc. 7th Annual Symposium on Combinatorial Pattern Matching, Lecture Notes in Comput. Sci. 1075, Springer-Verlag, Berlin, 1996, pp. 168-185.
3. A. CAPRARA, Sorting Permutations by Reversals and Eulerian Cycle Decompositions, Tech. report OR/97/4 DEIS, Università di Bologna Bologna, Italy, 1997.
4. A. CAPRARA, Formulations and Complexity of Multiple Sorting by Reversals, in Proc. Third Annual international Conference on Computational Molecular Biology (RECOMB'99), ACM Press, New York, 1999, to appear.
5. A. CAPRARA, On the Tightness of the Alternating-Cycle Lower Bound for Sorting by Reversals, J. Comb. Optim., to appear.
6. [G] A. CAPRARA, G. LANCIA, AND S.-K. NG, A Column-Generation Based Branch-and-Bound Algorithm for Sorting by Reversals, Tech. report OR/95/7 DEIS, Università di Bologna, Bologna, Italy, 1995; to appear in DIMACS Series in Discrete Mathematics and Theoretical Computer Science.
7. D. A. CHRISTIE, A 3/2 approximation algorithm for sorting by reversals, in Proc. the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, ACM Press, New York, 1998, pp. 244-252.
8. P. CRESCENZI AND V. KANN, A Compendium of NP Optimization Problems, Tech. report SI/RR-95/02, Dipartimento di Scienze dell'Informazione, Università di Roma "La Sapienza," 1995; also available online from http://www.nada.kth.se/theory/problemlist.html.
9. N. FRANKLIN, Conservation of genome form but not sequence in the transcription antitermination determinants of bacteriophages λ, φ21 and P22, J. Molecular Evolution, 181 (1985), pp. 75-84.
10. S. HANNENHALLI AND P. A. PEVZNER, Transforming cabbage into turnip (Polynomial algorithm for sorting signed permutations by reversals), in Proc. 27th Annual ACM Symposium on the Theory of Computing, ACM Press, New York, 1995, pp. 178-187.
11. S. HANNENHALLI AND P. A. PEVZNER, To cut ... or not to cut (Applications of comparative physical maps in molecular evolution), in Proc. 7th Annual ACM-SIAM Symposium on Discrete Algorithms, ACM Press, New York, 1996, pp. 304-313.
12. I. HOLYER, The NP-completeness of some edge-partition problems, SIAM J. Comput., 10 (1981), pp. 713-717.
13. R. W. IRVING AND D. A. CHRISTIE, Sorting by Reversals: A Conjecture of Kececioglu and Sankoff, Computer Science Dept. Tech report TR-1995-12, University of Glasgow, Glasgow, 1995.
14. H. KAPLAN, R. SHAMIR, AND R. E. TARJAN, Faster and simpler algorithm for sorting signed permutations by reversals, in Proc. 8th Annual ACM-SIAM Symposium on Discrete Algorithms, ACM Press, New York, 1997, pp. 344-351.
15. J. KECECIOGLU AND D. SANKOFF, Efficient bounds for oriented chromosome inversion distance, in Proc. 5th Annual Symposium on Combinatorial Pattern Matching, Lecture Notes in Comput. Sci. 807, Springer-Verlag, New York, Berlin, 1994, pp. 307-325.
16. J. KECECIOGLU AND D. SANKOFF, Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement, Algorithmica, 13 (1995), pp. 180-210.
17. P. A. PEVZNER AND M. S. WATERMAN, Open combinatorial problems in computational molecular biology, Proc. 3rd Israel Symposium on the Theory of Computing and Systems, IEEE Computer Society Press, Piscataway, NJ, 1995, pp. 158-172.
18. D. SANKOFF, Analytical approaches to genomic evolution, Biochimie, 75 (1993), pp. 409-413.
19. D. SANKOFF, G. LEDUC, N. ANTOINE, B. PAQUIN, B. F. LANG, AND R. CEDERGREN, Gene order comparisons for phylogenetic inference: Evolution of the mitochondrial genome, in Proc. Natl. Acad. Sci. U.S.A., 89 (1992), pp. 6575-6579.
20. N. TRAN, An Easy Case of Sorting by Reversals, in Proc. 8th Annual Symposium on Combinatorial Pattern Matching, Lecture Notes in Comput. Sci. 1264, Springer-Verlag, New York, Berlin, 1997, pp. 83-89.
21. G. A. WATTERSON, W. J. EWENS, T. E. HALL, AND A. MORGAN, The chromosome inversion problem, J. Theoret. Biology, 99 (1982), pp. 1-7.