Molecular Sticker Model Stimulation on Silicon for a Maximum Clique Problem
Abstract
:1. Introduction
2. Results
2.1. The Procedure of Experiment
Scanning Signals | Value | Addressing Signals | Value |
---|---|---|---|
X0 | Y0 | ||
X1 | Y1 | ||
X2 | Y2 | ||
X3 | Y3 | ||
X4 | Y4 | ||
X5 | Y5 | ||
X6 | Y6 | ||
X7 | Y7 | ||
X8 | Y8 | ||
X9 | Y9 | ||
X10 | Y10 | ||
X11 | Y11 | ||
X12 | Y12 | ||
X13 | Y13 | ||
X14 | Y14 | ||
X15 | Y15 |
Steps | Operation | Meaning |
---|---|---|
1 | 1.SW ******** 0 | Sub-graphs with edges E1 are set to be 1 at 1th subfield |
2.SW 1*1***** 1 | ||
2 | 1.SW ******** 0 | Sub-graphs with edges E2 are set to be 1 at 2th subfield |
2.SW 1**1**** 1 | ||
··· | ··· | ··· |
12 | 1.SW ******** 0 | Sub-graphs with edges E12 are set to be 1 at 12th subfield |
2.SW *****11*1 | ||
13 | SW 11****** 0 | Eliminate sub-graphs with edges e1 in the complementary graph at 13th subfield |
14 | SW 1******1 0 | Eliminate sub-graphs with edges e2 in the complementary graph at 13th subfield |
··· | ··· | ··· |
28 | SW ******11 0 | Eliminate sub-graphs with edges e16 in the complementary graph at 13th subfield |
2.2. Time Complexity of the Algorithm
2.3. Space Complexity of the Algorithm
2.4. Comparison with Previous Studies
3. DNA-Based Sticker Model
3.1. Representation of Information
3.2. Operations on Sets of Strings
4. DNA Electronic Computing Model (DEM) Method
4.1. Representation of Information
4.2. Processing of Information
4.3. Computation of DEM
4.4. Example of DEM Computing
5. Architecture of DEM
5.1. Plasma Display Panel (PDP) Display Model
5.2. Control Model
Instructions | Machine Code | Meaning |
---|---|---|
(SR, V, d) | 0001Vd | Read data from the selected memories |
(SW, V, d) | 0010Vd | Write data to the selected memories |
5.2.1. Scan-Driving Controller
5.2.2. Address-Driving Controller
5.3. Result-Analyzing Model
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
- Adleman, L. Molecular computation of solutions to combinational problems. Science 1994, 266, 1021–1024. [Google Scholar] [CrossRef] [PubMed]
- Roweis, S.; Winfree, E.; Burgoyne, R.; Chelyapov, N.V.; Goodman, M.F.; Rothemund, P.W.K.; Adleman, L. A sticker-based model for DNA computation. J. Comput. Biol. 1998, 5, 615–629. [Google Scholar] [CrossRef] [PubMed]
- Head, T. Formal language theory and DNA: An analysis of the generative capacity of specific recombinant behaviors. Bull. Math. Biol. 1987, 49, 737–759. [Google Scholar] [CrossRef] [PubMed]
- Freund, R.; Kari, L.; Paun, G. DNA computing based on splicing: The existence of universal computers. Theor. Comput. Syst. 1999, 32, 69–112. [Google Scholar] [CrossRef]
- Benenson, Y.; Paz-Elizur, T.; Adar, R.; Keinan, E.; Livneh, Z.; Shapiro, E. Programmable and autonomous computing machine made of biomolecules. Nature 2001, 414, 430–434. [Google Scholar] [CrossRef] [PubMed]
- Sakamoto, K.; Gouzu, H.; Komiya, K.; Kiga, D.; Yokoyama, S.; Yokomori, T.; Hagiya, M. Molecular computation by DNA hairpin formation. Science 2000, 288, 1223–1226. [Google Scholar] [CrossRef] [PubMed]
- Head, T.; Rozenberg, G.; Bladergroen, R.S.; Breek, C.K.D.; Lommerse, P.H.M.; Spaink, H.P. Computing with DNA by operating on plasmids. Biosystems 2000, 57, 87–93. [Google Scholar] [CrossRef]
- Liu, W.B.; Gao, L.; Zhang, Q.; Xu, G.D.; Zhu, X.G.; Liu, X.R.; Jin, X. A random walk DNA algorithm for the 3-SAT problem. Curr. Nanosci. 2005, 1, 85–90. [Google Scholar] [CrossRef]
- Winfree, E.; Liu, FR.; Wenzler, L.A.; Seeman, N.C. Design and self-assembly of two-dimensional DNA crystals. Nature 1998, 394, 539–544. [Google Scholar] [CrossRef] [PubMed]
- Qian, L.; Winfree, E. Scaling up digital circuit computation with DNA strand displacement cascades. Science 2011, 332, 1196–1201. [Google Scholar] [CrossRef] [PubMed]
- Qian, L.; Winfree, E.; Bruck, J. Neural network computation with DNA strand displacement cascades. Nature 2011, 475, 368–372. [Google Scholar] [CrossRef] [PubMed]
- Ouyang, Q.; Kaplan, P.D.; Liu, S.M.; Libchaber, A. DNA solution of the maximal clique problem. Science 1997, 278, 446–449. [Google Scholar] [CrossRef] [PubMed]
- Braich, R.S.; Chelyapov, N.; Johnson, C.; Rothemund, P.W.K.; Adleman, L. Solution of a 20-variable 3-SAT problem on a DNA computer. Science 2002, 296, 499–502. [Google Scholar] [CrossRef] [PubMed]
- Gao, L.; Ma, R.N.; Xu, J. DNA solution of vertex cover problem based on sticker model. Chin. J. Electron. 2002, 11, 280–284. [Google Scholar]
- Zimmermanm, K.H. Efficient DNA sticker algorithms for NP-complete graph problems. Comput. Phys. Commun. 2002, 144, 297–309. [Google Scholar] [CrossRef]
- Mertzios, G.B. An intersection model for multitolerance graphs: Efficient algorithms and hierarchy. Algorithmica 2002, 69, 540–581. [Google Scholar] [CrossRef] [Green Version]
- Chang, W.L.; Vasilakos, A.V. DNA algorithms of implementing biomolecular databases on a biological computer. IEEE Trans. Nanobiosci. 2015, 14, 104–111. [Google Scholar] [CrossRef]
- Chang, W.L.; Ren, T.T.; Mang, F. Quantum algorithms and mathematical formulations of bio-molecular solutions of the vertex cover problem in the finite-dimensional Hilbert space. IEEE Trans. Nanobiosci. 2015, 14, 121–128. [Google Scholar] [CrossRef] [PubMed]
- Chang, W.L. Fast parallel DNA-based algorithms for molecular computation: Quadratic congruence and factoring integers. IEEE Trans. Nanobiosci. 2012, 11, 62–69. [Google Scholar] [CrossRef] [PubMed]
- Chang, W.L.; Vasilakos, A.V. Molecular Computing: Towards a Novel Computing Architecture for Complex Problem Solving (Studies in Big Data); Springer: Berlin, Germany, 2014. [Google Scholar]
- Chang, W.L.; Ren, T.T.; Luo, J.; Mang, F. Quantum algorithms for bio-molecular solutions of the satisfiability problem on a quantum machine. IEEE Trans. Nanobiosci. 2008, 7, 215–222. [Google Scholar] [CrossRef] [PubMed]
- Chang, W.L. Fast parallel DNA-based algorithms for molecular computation: The set-partition problem. IEEE Trans. Nanobiosci. 2007, 6, 346–353. [Google Scholar] [CrossRef]
- Chang, W.L.; Michael, H.; Minyi, G. Fast parallel molecular algorithms for DNA-based computation: Factoring integers. IEEE Trans. Nanobiosci. 2005, 4, 149–163. [Google Scholar] [CrossRef]
- Martinez-Perez, I.; Brandt, W.; Wild, M.; Zimmermann, K.H. Bioinspired parallel algorithms for maximum clique problem on FPGA architectures. J. Signal Proc. Syst. 2010, 58, 117–124. [Google Scholar] [CrossRef]
- Li, Y.M.; Yu, W.; Ning, J.G. Generalized molecular computational model for NP problems. Appl. Res. Comput. 2014, 31, 3353–3356. [Google Scholar]
- Yang, Z.; Ma, T.B.; Yu, W.; Li, Y.M.G. Application of generalized molecular computation model in 0–1 knapsack problem. Comput. Sci. 2014, 41, 7–9. [Google Scholar]
- Martinez-Perez, I.M.; Zimmermann, K.H. Parallel bioinspired algorithms for NP complete graph problems. J. Parallel Distrib. Comput. 2009, 69, 221–229. [Google Scholar] [CrossRef]
- Ho, M.; Chang, W.L.; Guo, M.Y.; Yang, L.T. Fast parallel solution for set-packing and clique problem by DNA-based computing. IEICE. Trans. Inf. Syst. 2004, E87, 1782–1788. [Google Scholar]
- Darehmiraki, M. A new solution for maximal clique problem based sticker model. Biosystems 2009, 95, 145–149. [Google Scholar] [CrossRef] [PubMed]
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Ning, J.; Li, Y.; Yu, W. Molecular Sticker Model Stimulation on Silicon for a Maximum Clique Problem. Int. J. Mol. Sci. 2015, 16, 13474-13489. https://doi.org/10.3390/ijms160613474
Ning J, Li Y, Yu W. Molecular Sticker Model Stimulation on Silicon for a Maximum Clique Problem. International Journal of Molecular Sciences. 2015; 16(6):13474-13489. https://doi.org/10.3390/ijms160613474
Chicago/Turabian StyleNing, Jianguo, Yanmei Li, and Wen Yu. 2015. "Molecular Sticker Model Stimulation on Silicon for a Maximum Clique Problem" International Journal of Molecular Sciences 16, no. 6: 13474-13489. https://doi.org/10.3390/ijms160613474