Two applications of the Divide&Conquer principle in the molecular sciences

Mathematical Programming, Series B

Volumn 79, Issue 1-3, 1997, Pages 71-97

  Brinkmann, G ^a   Dress, A W M ^a   Perrey, S W ^a   Stoye, J ^a  

^a BIELEFELD UNIVERSITY   (Germany)

Author keywords

Divide Conquer; Fullerenes; Multiple sequence allignment; Structure enumeration

Indexed keywords

EID: 17744385967     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02614312     Document Type: Article

References (49)

1. S.F. Altschul, Gap costs for multiple sequence alignment, J. Theor. Biol. 138 (1989) 297-309.
2. S.F. Altschul, R.J. Carroll and D.J. Lipman, Weights for data related by a tree, J. Mol. Biol. 207 (1989) 647-653.
3. 60, Kekule counts versus stability, Chem. Phys. Letters 228 (1994) 478-484.
4. D. Babić, G. Brinkmann and A. Dress, Topological resonance energy of fullerenes (1997) in preparation.
5. G. Brinkmann, The combinatorial enumeration of tube-type Fullerenes and Fullerene caps, (1997) in preparation.
6. G. Brinkmann and A.W.M. Dress, A constructive enumeration of fullerenes, Journal of Algorithms (1997) to appear.
7. H. Carrillo and D.J. Lipman, The multiple sequence alignment problem in biology, SIAM J. Appl. Math. 48 (5) (1988) 1073-1082.
8. S.C. Chan, A.K.C. Wong and D.K.Y. Chiu, A survey of multiple sequence comparison methods, Bull. Math. Biol. 54 (4) (1992) 563-598.
9. H.S.M. Coxeter, Regular Polytopes (Dover, New York, 1973).
10. M.O. Dayhoff, R.M. Schwartz and B.C. Orcutt, A model of evolutionary change in proteins, in: M.O. Dayhoff, ed., Atlas of Protein Sequences and Structure, Vol. 5, Suppl. 3 (National Biomedical Research Foundation, Washington, DC, 1979) 345-352.
11. R.F. Doolittle, Computer methods for macromolecular sequence analysis, Methods in Enzymology 266 (Academic Press, San Diego, USA, 1996).
12. A.W.M. Dress and M. Krüger, Parsimonious phylogenetic trees in metric spaces and simulated annealing, Adv. in Appl. Math. 8 (1987) 8-37.
13. A.W.M. Dress, On the computational complexity of composite systems, Proceedings of the Ninth Sitges Conference in Theoretical Physics, Sitges, 1986 Springer Lecture Notes, Vol. 268 (Springer, Berlin, 1987) 377-388.
14. A.W.M. Dress, Computing spin-glass Hamiltonians, Manuscript, Bielefeld, 1986.
15. A.W.M Dress, G. Füllen and S.W. Perrey, A divide and conquer approach to multiple aLignment, in: Proceedings of the Third Conference on Intelligent Systems for Molecular Biology, ISMB 95 (AAAI Press, Menlo Park, CA, USA, 1995) 107-113.
16. D.-F. Feng and R.F. Doolittle, Progressive sequence alignment as a prerequisite to correct phylogenetic trees, J. Mol. Evol. 21 (1987) 112-125.
17. O. Gotoh, An improved algorithm for matching biological sequences, J. Mol. Biol. 162 (1981) 705-708.
18. S.K. Gupta, J.D. Kececioglu and A.A. Schäffer, Improving the practical space and time efficiency of the shortest-paths approach to sum-of-pairs multiple sequence alignment, J. Comp. Biol. 2 (3) (1995) 459-472.
19. T. Harmuth, Die Generierung simpler, 3-regulärer planarer, zusammenhängender Graphen mit vorgegebenen Flächengrößen, Diplomarbeit, Universität Bielefeld, 1997.
20. R.E. Hickson, C. Simon and S.W. Perrey, An evaluation of multiple sequence alignment programs using an rRNA data set, (1997) submitted.
21. D.S. Hirschberg, A linear space algorithm for computing maximal common subsequences, Communications of the ACM 18 (6) (1975) 341-343.
22. D.J. Klein and X. Liu, Elemental carbon isomerism, in: International Journal of Quantum Chemistry, Quantum Chemistry Symposium 28 (John Wiley & Sons, New York, 1994) 501-523.
23. 60: Buckminsterfullerene, Nature 318 (1985) 162-163.
24. D.J. Lipman, S.F. Altschul and J.D. Kececioglu, A tool for multiple sequence alignment, Proc. Nat. Acad. Sci. USA 86 (1989) 4412-4415.
25. X. Liu, D.J. Klein, T.G. Schmalz and W.A. Seitz, Sixty-atom carbon cages, Journal of Computational Chemistry 12 (10) (1991) 1265-1269.
26. J. Malkevitch, Polytopal graphs, in: L.W. Beineke and R.J. Wilson, eds., Selected Topics in Graph Theory, Vol. 3 (1988) 169-188.
27. H.M. Martinez, A flexible multiple sequence alignment program, Nucl. Acids Res. 16 (1988) 1683-1691.
28. D.E. Manolopoulos and P.W. Fowler, An Atlas of Fullerenes (Oxford University Press, Oxford, 1995).
29. 70, Chemical Physics Letters 181 (2-3) (1991) 105-111.
30. M.A. McClure, T.K. Vasi and W.M. Fitch, Comparative analysis of multiple protein-sequence alignment methods, J. Mol. Biol. Evol. 11 (4) (1994) 571-592.
31. E.W. Myers and W. Miller, Optimal alignments in linear space, CABIOS 4 (1) (1988) 11-17.
32. E.W. Myers, An overview of sequence comparison algorithms in molecular biology, Technical Report TR 91-29, Department of Computer Science, University of Arizona, Tucson, 1991.
33. S.B. Needleman and C.D. Wunsch, A general method applicable to the search for similarities in the amino acid sequence of two proteins, J. Mol. Biol. 48 (1970) 443-453.
34. S.W. Perrey, M.D. Hendy and R.E. Hickson, Evaluating the bias of multiple sequence alignment methods for phylogenetic tree reconstruction, Manuscript, Christchurch, 1997.
35. S.W. Perrey and J. Stoye, Fast approximation to the np-hard problem of multiple sequence alignment, Information and Mathematical Sciences Reports, Series B:96/06 (ISSN 1171-7637), May 1996.
36. S.W. Perrey, J. Stoye, V. Moulton and A.W.M. Dress, On simultaneous versus iterative multiple sequence alignment, (1997) submitted.
37. M.J. Plunkett and J.A. Ellman, Combinatorial chemistry and new drugs, Scientific American 276 (4) (1997) 54-59.
38. Chih-Han Sah, Combinatorial construction of fullerene structures, Croatica Chemica Acta (1993) 1-12.
39. D. Sankoff and J.B. Kruskal, eds., Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison (Addison Wesley, Reading, MA, 1983).
40. T.G. Schmalz, W.A. Seitz, D.J. Klein and G.E. Hite, Elemental carbon cages, J. Amer. Chem. Soc. 110 (1988) 1113-1127.
41. J. Stoye, Divide and conquer multiple sequence alignment, http://bibiserv.techfak.uni-bielefeld.de/dca/, 1996.
42. J. Stoye, S.W. Perrey and A.W.M. Dress, Improving the divide-and-conquer approach to sum-of-pairs multiple sequence alignment, Appl. Math. Lett. (1997) to appear.
43. J. Stoye, Divide-and-conquer multiple sequence alignment, Dissertation, Technische Fakultät der Universität Bielefeld, 1997.
44. W.R. Taylor, Identification of protein sequence homology by consensus template alignment, J. Mol. Biol. 188, pp. 233-258
45. J.D. Thompson, D.G. Higgins and T.J. Gibson, CLUSTAL W: Improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice, Nucl. Acids Res. 22 (1994) 4673-4680.
46. U. Tönges, S.W. Perrey, J. Stoye and A.W.M. Dress, A general method for fast multiple sequence alignment, Gene 172 (1996) GC33-GC41.
47. M. Vingron and P. Argos, Motif recognition and alignment for many sequences by comparison of dotmatrices, J. Mol. Biol. 218 (1991) 33-43.
48. R.A. Wagner and M.J. Fischer, The string-to-string correction problem, Journal of the ACM 21 (1) (1974) 168-173.
49. M.S. Waterman, Introduction to Computational Biology. Maps Sequences and Genomes (Chapman & Hall, London, UK, 1995).