On the scalability of biocomputing algorithms: The case of the maximum clique problem

Theoretical Computer Science

Volumn 412, Issue 51, 2011, Pages 7075-7086

  Manrique, Daniel ^a   Rodríguez Patón, Alfonso ^a   Sosík, Petr ^a,b  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b SILESIAN UNIVERSITY IN OPAVA   (Czech Republic)

Author keywords

Breadth first search; DNA computing; Error resistance; Maximum clique problem

Indexed keywords

BIOINFORMATICS; CALCULATIONS; DNA; SCALABILITY;

BIO-COMPUTING ALGORITHMS; BIO-MOLECULAR; BREADTH-FIRST SEARCH; DNA ALGORITHMS; DNA-COMPUTING; MAXIMUM CLIQUE PROBLEMS; PROCESS GRAPHS; PRUNING TECHNIQUES;

PARAMETER ESTIMATION;

EID: 80455176990     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2011.09.004     Document Type: Article

References (36)

1. L.M. Adleman Molecular computation of solutions to combinatorial problems Science 266 1994 1021 1024 (Pubitemid 24373714)
2. B.M. Alberts Efficient separation of single-stranded and double-stranded deoxyribonucleic acid in a dextran-polyethylene glycol two-phase system Biochemistry 6 8 1967 2527 2532
3. M. Amos, A. Gibbons, D. Hodgson, Error-resistant implementation of DNA computations, in: [22], 1996 pp. 87101.
4. M. Amos Theoretical and Experimental DNA Computation 2005 Springer-Verlag
5. M. Amos R.A. Meyers, DNA Computing Encyclopedia of Complexity and Systems Science 2009 Springer Berlin 2089 2104
6. M. Arita, and S. Kobayashi DNA sequence design using templates New Generation Computing 20 2002 263 277 (Pubitemid 34777521)
7. E. Bach, A. Condon, E. Glaser, and C. Tanguay DNA models and algorithms for NP-complete problems Journal of Computer and System Sciences 57 1998 172 186 (Pubitemid 128413163)
8. T. Bck, J.N. Kok, G. Rozenberg, Evolutionary computation as a paradigm for DNA-based computing, in: L. Landweber, E. Winfree, R. Lipton, and S. Freeland (Eds.), Proceedings: DIMACS Workshop on Evolution as Computation, Princeton, NJ, 1999, pp. 6788.
9. E.B. Baum, D. Boneh, Running dynamic programming algorithms on a DNA computer, in: [22], 1996, pp. 141147.
10. I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo The Maximum Clique Problem D.Z. Du, P.M. Pardalos, Handbook of Combinatorial Optimization, Supplement Volume A 1999 Kluwer Dordrecht 1 74
11. D. Boneh, C. Dunworth, R. Lipton, J. Sgall, Making DNA computers error resistant, in: [22], 1996, pp. 102110.
12. Y. Benenson, B. Gil, U. Ben-dor, R. Adar, and E. Shapiro An autonomous molecular computer for logical control of gene expression Nature 429 2004 423 429 (Pubitemid 38715134)
13. A.R. Cukras, D. Faulhammer, R.J. Lipton, and L.F. Landweber Chess games: a model for RNA based computation Biosystems 52 1999 35 45 (Pubitemid 29518347)
14. K.A. Eckert, and T.A. Kunkel DNA polymerase fidelity and the polymerase chain reaction PCR Methods Applications 1 1991 17 24
15. K. Fujibayashi, D.Y. Zhang, E. Winfree, and S. Murata Error suppression mechanisms for DNA tile self-assembly and their simulation Natural Computing 8 3 2009 589 612
16. M. García-Arnau, D. Manrique, A. Rodríguez-Patón, and P. Sosík A P system and a constructive membrane-inspired DNA algorithm for solving the maximum clique problem Biosystems 90 3 2007 687 697 (Pubitemid 350026181)
17. R.L. Graham, D.E. Knuth, and O. Patashnik Concrete Mathematics 1992 Addison-Wesley Reading
18. T. Head, M. Yamamura, S. Gal, Aqueous computing: writing on molecules, in: Proceedings of Congress on Evolutionary Computation, IEEE Service Center, Piscataway, NJ, 1999, pp. 10061010.
19. S.N. Ho, H.D. Hunt, R.M. Horton, J.K. Pullen, and L.R. Pease Site-directed mutagenesis by overlap extension using the polymerase chain reaction Gene 77 1 1989 51 59 (Pubitemid 19125653)
20. S. Janson, T. Luczak, and A. Rucinski Random Graphs 2000 John Wiley & Sons
21. R. Jungmann, S. Renner, and F. Simmel From DNA nanotechnology to synthetic biology HFSP Journal 2 2008 99 109
22. L.B Landweber, and E.B. Baum Second Annual Workshop on DNA Based Computers, Princeton University, NJ, USA, June 1012, 1996 1996 American Mathematical Society
23. K. Li, X. Zhou, and S. Zou Improved volume molecular solutions for the maximum clique problem on DNA-based supercomputing Chinese Journal of Computers 31 12 2008 2173 2181
24. V. Manca, and C. Zandron A clause string DNA algorithm for SAT Lecture Notes in Computer Science 2340 2001 Springer-Verlag 172 181
25. D.W. Matula, On the complete subgraphs of a random graph, in: R.C. Bose, et al. (Eds.), Proc. 2nd Chapel Hill Conf. Combinatorial Math. and its Applications, Univ. North Carolina, Chapel Hill, 1970, pp. 356369.
26. A. Narayanan, S. Zorbalas, DNA algorithms for computing shortest paths, in: J.R. Koza, et al. (Eds.), Genetic Programming 1998: Proceedings of the Third Annual Conference, 1998, pp. 718724.
27. M. Ogihara, and A. Ray DNA-based parallel computation by counting H. Rubin, D.H. Wood, DNA Based Computers III 1997 255 264
28. Q. Ouyang, Peter D. Kaplan, S. Liu, and A. Libchaber DNA solution of the maximal clique problem Science 278 1997 446 449 (Pubitemid 27454425)
29. W. Pullan, F. Mascia, and M. Brunato Cooperating local search for the maximum clique problem Journal of Heuristics 2010 1 19 (online) http://dx.doi.org/10.1007/s10732-010-9131-5
30. Z.F. Qiu, and M. Lu A new approach to advance the DNA computing Applied Soft Computing 3 2003 177 189 (Pubitemid 40442497)
31. G. Pun, G. Rozenberg, and A. Salomaa DNA Computing. New Computing Paradigms 1998 Springer-Verlag
32. J.A. Rose, M. Hagiya, R.J. Deaton, and A. Suyama A DNA-based in vitro genetic program Journal of Biological Physics 28 3 2002 493 498 (Pubitemid 35256962)
33. E. Tomita, and T. Kameda An efficient branch-and-bound algorithm for finding a maximum clique with computational experiments Journal of Global Optimization 37 1 2007 95 111 (Pubitemid 44876770)
34. X. Wang, Z. Bao, J. Hu, and D. Gou DNA computing solves the 3-SAT problem with a small solution space Current Nanoscience 4 4 2008 354 360
35. H. Yoshida, and A. Suyama Solution to 3-SAT by breadth first search E. Winfree, D.K. Gifford, DNA Based Computers V DIMACS Series in Discrete Mathematics and Theoretical Computer Science vol. 54 2000 9 22
36. K.H. Zimmermann Efficient DNA sticker algorithms for NP-complete graph problems Computer Physics Communications 144 2002 297 309