Exploring the solution space of sorting by reversals, with experiments and an application to evolution

IEEE/ACM Transactions on Computational Biology and Bioinformatics

Volumn 5, Issue 3, 2008, Pages 348-356

  Braga, Marília D V ^a   Sagot, Marie France ^a,b   Scornavacca, Celine ^c   Tannier, Eric ^a,b  

^a UNIVERSITÉ LYON 1   (France)

^b INRIA RHÔNE ALPES   (France)

^c LIRMM   (France)

Author keywords

Common intervals; Computational biology; Evolution; Genome rearrangements; Perfect sorting; Signed permutations; Sorting by reversals

Indexed keywords

CHLORINE COMPOUNDS; CHROMOSOMES; EQUIVALENCE CLASSES; MAMMALS; MATHEMATICAL TRANSFORMATIONS; OPTIMAL SYSTEMS; SET THEORY;

COMMON INTERVALS; COMPARATIVE GENOMICS; COMPUTATIONAL BIOLOGY; ENUMERATION METHOD; EVOLUTION; GENOME REARRANGEMENTS; OPEN PROBLEMS; OPTIMAL SOLUTIONS; PERFECT SORTING; SEX CHROMOSOMES; SIGNED PERMUTATIONS; SOLUTION SPACES; SORTING BY REVERSALS;

SOLUTIONS;

MAMMALIA;

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; CHROMOSOME MAP; COMPUTER SIMULATION; DNA SEQUENCE; GENETICS; GENOMIC INSTABILITY; METHODOLOGY; MOLECULAR EVOLUTION; NUCLEOTIDE SEQUENCE;

ALGORITHMS; CHROMOSOME MAPPING; COMPUTER SIMULATION; DNA MUTATIONAL ANALYSIS; EVOLUTION, MOLECULAR; GENOMIC INSTABILITY; MODELS, GENETIC; SEQUENCE ANALYSIS, DNA;

EID: 49249120896     PISSN: 15455963     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCBB.2008.16     Document Type: Conference Paper

References (24)

1. Y. Ajana, J.F. Lefebvre, E. Tillier, and N. El-Mabrouk, "Exploring the Set of All Minimal Sequences of Reversals-An Application to Test the Replication-Directed Reversal Hypothesis," Proc. Second Int'l Workshop Algorithms in Bioinformatics (WABI '02), vol. 2452, pp. 300-315, 2002.
2. D.A. Bader, B.M.E. Moret, and M. Yan, "A Linear-Time Algorithm for Computing Inversion Distances Between Signed Permutations with an Experimental Study," J. Computational Biology, vol. 8, no. 5, pp. 483-491, 2001.
3. S. Berard, A. Bergeron, and C. Chauve, "Conserved Structures in Evolution Scenarios," RCG 2004, Lecture Notes in Bioinformatics, vol. 3388, pp. 1-15, 2005.
4. S. Berard, A. Bergeron, C. Chauve, and C. Paul, "Perfect Sorting by Reversals Is Not Always Difficult," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 4, no. 1, pp. 4-16, Jan.-Mar. 2007.
5. A. Bergeron, C Chauve, T. Hartmann, and K. St-Onge, "On the Properties of Sequences of Reversals That Sort a Signed Permutation," Proc. Journées Ouvertes Biologie, Informatique et Mathématiques (JOBIM '02), pp. 99-108, 2002.
6. A. Bergeron, S. Heber, and J. Stoye, "Common Intervals and Sorting by Reversals: A Marriage of Necessity," Bioinformatics, vol. 18 (Suppl. 2), pp. S54-63, 2002.
7. A. Bergeron, J. Mixtacki, and J. Stoye, "The Inversion Distance Problem," Math, of Evolution and Phylogeny, O. Gascuel, ed., pp. 262-290, Oxford Univ. Press, 2005.
8. M.D.V Braga, M.-F. Sagot, C. Scornavacca, and E. Tannier, "The Solution Space of Sorting by Reversals," Proc. Int'l Symp. Bioinformatics Research and Applications (ISBRA '07), vol. 4463, pp. 293-304, 2007.
9. G. Brightwell and P. Winkler, "Counting Linear Extensions is #P-Complete," Proc. 23rd Ann. ACM Symp. Theory of Computing (STOC), 1991.
10. The Book of Traces, V. Diekert, G. Rozenberg, eds. World Scientific, 1995.
11. Y. Diekmann, M.F. Sagot, and E. Tannier, "Evolution under Reversals: Parsimony and Conservation of Common Intervals," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 4, no. 2, pp. 301-309, Apr.-June 2007. (A preliminary version appeared in COCOON 2005, LNCS 3595, 42-51, 2005.)
12. R.P. Dilworth, "A Decomposition Theorem for Partially Ordered Sets," Annals of Math., vol. 51, pp. 161-166, 1950.
13. D.R. Fulkerson, "Note on Dilworth's Decomposition Theorem for Partially Ordered Sets," Proc. Am. Math. Soc., vol. 7, pp. 701-702, 1956.
14. Y. Han, "Improving the Efficiency of Sorting by Reversals," Proc. Int'l Conf. Bioinformatics and Computational Biology, 2006.
15. S. Hannenhalli and P. Pevzner, "Transforming Cabbage into Turnip (Polynomial Algorithm for Sorting Signed Permutations by Reversals)," J. ACM, vol. 46, pp. 1-27, 1999.
16. B.T. Lahn and D.C. Page, "Four Evolutionary Strata on the Human X Chromosome," Science, vol. 286, pp. 964-967, 1999.
17. Z. Li, L. Wang, and K. Zhang, "Algorithmic Approaches for Genome Rearrangement: A Review," IEEE Trans. Systems, Man, and Cybernetics, vol. 36, pp. 636-648, 2006.
18. S. Ohno, Sex Chromosomes and Sex-Linked Genes. Springer, 1967.
19. M.T. Ross et al., "The DNA Sequence of the Human X Chromosome," Nature, vol. 434, pp. 325-337, 2005.
20. A. Siepel, "An Algorithm to Enumerate Sorting Reversals for Signed Permutations," J. Computational Biology, vol. 10, pp. 575-597, 2003.
21. H. Skaletsky et al., "The Male-Specific Region of the Human Y Chromosome is a Mosaic of Discrete Sequence Classes," Nature, vol. 423, pp. 825-837, 2003.
22. G. Steiner, "An Algorithm to Generate the Ideals of a Partial Order," Operations Research Letters, vol. 5, no. 6, pp. 317-320, 1986.
23. G. Steiner, "Polynomial Algorithms to Count Linear Extensions in Certain Posets," Congressus Numcrantium, vol. 75, pp. 71-90, 1990.
24. E. Tannier, A. Bergeron, and M.-F. Sagot, "Advances on Sorting by Reversals," Discrete Applied Math., vol. 155, nos. 6-7, pp. 881-888, 2007.