Citation:  CUI Jianzhong, YIN Zhixiang, TANG Zhen, YANG Jing. Probe Machine Based Computing Model for Maximum Clique Problem[J]. Chinese Journal of Electronics, 2022, 31(2): 304312. doi: 10.1049/cje.2020.00.293 
[1] 
J. Xie, W Kong, L Pang, et al., “Staggered grid scheme for the FFTbased methods,” Chinese Journal of Electronics, vol.28, no.5, pp.1066–1072, 2019. doi: 10.1049/cje.2019.06.002

[2] 
N. Zhang and T. Zhang, “Recurrent neural networks for computing the moorepenrose inverse with momentum learning,” Chinese Journal of Electronics, vol.29, no.6, pp.1039–1045, 2020. doi: 10.1049/cje.2020.02.005

[3] 
L. Yang, G Hu, C Zhang, et al., “Solving structured nonlinear programming based on CPUGPU collaborative parallel interior point algorithm,” Chinese Journal of Electronics, vol.47, no.2, pp.382–389, 2019.

[4] 
M. Yue and B. Bai, “Design and implementation of DSP system for motor FOC algorithm,” Chinese Journal of Electronics, vol.48, no.10, pp.2041–2046, 2020.

[5] 
J. Liu, Y. Ge, M. Tian, et al., “ZYNQbased reconfigurable convolutional neural network accelerator,” Chinese Journal of Electronics, vol.49, no.4, pp.729–735, 2021.

[6] 
N. Hou, F. He, Y. Zhou, et al., “An efficient GPUbased parallel tabu search algorithm for hardware/software codesign,” Frontiers of Computer Science, vol.14, no.5, pp.1–18, 2020.

[7] 
Y. Zhou, F. He, N. Hou, et al., “Parallel ant colony optimization on multicore SIMD CPUs,” Future Generation Computer Systems, vol.79, no.2, pp.473–487, 2018.

[8] 
Y. Zhou, F. He, and Y. Qiu, “Accelerating image convolution filtering algorithms on integrated CPUGPU architectures,” Journal of Electronic Imaging, vol.27, article no.033002, 2018. doi: 10.1117/1.JEI.27.3.033002

[9] 
Y. Zhou, F. He, and Y. Qiu, “Dynamic strategy based parallel ant colony optimization on GPUs for TSPs,” Science China Information Sciences, vol.60, article no.068102, 2017. doi: 10.1007/s1143201505942

[10] 
D. Deutsch, “Quantum theory, the ChurchTuring principle and the universal quantum computer,” Proc. of the Royal Society of London A, vol.400, no.1818, pp.97–117, 1985. doi: 10.1098/rspa.1985.0070

[11] 
M. Muller, “Strongly universal quantum turing machines and invariance of Kolmogorov complexity,” IEEE Trans. on Information Theory, vol.54, no.2, pp.763–780, 2008. doi: 10.1109/TIT.2007.913263

[12] 
Frank Tabakin, “Model dynamics for quantum computing,” Annals of Physics, vol.383, pp.33–78, 2017. doi: 10.1016/j.aop.2017.04.013

[13] 
W. S. Mcculloch and W. Pitts, “A logical calculus of the ideas immanent in nervous activity,” Bulletin of Mathematical Biology, vol.5, pp.115–133, 1943. doi: 10.1007/BF02478259

[14] 
Z. Aram, S. Jafari, J. Ma, et al., “Using chaotic artificial neural networks to model memory in the brain,” Communications in Nonlinear Science and Numerical Simulation, vol.44, pp.449–459, 2017. doi: 10.1016/j.cnsns.2016.08.025

[15] 
M. Ranjbar, S. Effati, and S. M. Miri, “An artificial neural network for solving quadratic zeroone programming problems,” Neurocomputing, vol.235, pp.192–198, 2017.

[16] 
L. Adleman, “Molecular computation of solutions to combinatorial problems,” Science, vol.266, no.5187, pp.1021–1024, 1994. doi: 10.1126/science.7973651

[17] 
Z. X. Yin, J. Z. Cui, and J. Yang, “Integer programming problem based on plasmid DNA computing model,” Chinese Journal of Electronics, vol.26, no.6, pp.1284–1288, 2017. doi: 10.1049/cje.2017.07.013

[18] 
T. Song, P. Zheng, W. M. L. Dennis, et al., “Design of logic gates using spiking neural P systems with homogeneous neurons and astrocyteslike control,” Information Sciences, vol.372, pp.380–391, 2016.

[19] 
X. Wang, T. Song, F. Gong, et al., “On the computational power of spiking neural P systems with selforganization,” Scientific Reports, vol.6, no.1, pp.27624–27639, 2016. doi: 10.1038/srep27624

[20] 
H. Peng, J. Yang, J. Wang, et al., “Spiking neural P systems with multiple channels,” Neural Networks, vol.95, pp.66–71, 2017.

[21] 
J. Xu, “Probe machine,” IEEE Transactions on Neural Networks & Learning Systems, vol.27, no.7, pp.1405–1416, 2016.

[22] 
R. M. Karp. “Reducibility among combinatorial problems,” in Complexity of Computer Computations, R. E. Miller and J. W. Thatcher, edit., New York: Plenum Press, pp.88−103, 1972.

[23] 
C. Godsil and B. Rooney, “Hardness of computing clique number and chromatic number for Cayley graphs,” European Journal of Combinatorics, vol.62, pp.147–166, 2017.

[24] 
R. D. Luce and A. D. Perry, “A method of matrix analysis of group structure,” Psychometrika, vol.14, no.2, pp.95–116, 1949. doi: 10.1007/BF02289146

[25] 
F. Harary and I. C. Ross, “A procedure for clique detection using the group matrix,” Sociometry, vol.20, no.3, pp.205–215, 1957. doi: 10.2307/2785673

[26] 
D. E. Knuth, The Art of Computer Programming, 1st ed., AddisonWesley Professional, 2011.

[27] 
A. H. Land, “An automatic method of solving discrete programming problem,” Econometrica, vol.28, no.3, pp.497–520, 1960. doi: 10.2307/1910129

[28] 
P. S. Segundo, A. Lopez, and P. M. Pardalos, “A new exact maximum clique algorithm for large and massive sparse graphs,” Computers & Operations Research, vol.66, pp.81–94, 2016.

[29] 
C. M. Li, H. Jiang, and F. Manyà, “On minimization of the number of branches in branchandbound algorithms for the maximum clique problem,” Computers & Operations Research, Vol.84, DOI: 10.1016/j.cor.2017.02.017, 2017.

[30] 
R. Kopf and G. Ruhe, “A computational study of the weighted independent set problem for general graphs,” Foundations of Control Engineering, vol.12, no.4, pp.167–180, 1987.

[31] 
S. Zhang, W. Jing, Q. Wu, et al., “A fast genetic algorithm for solving the maximum clique problem,” 2014 10th International Conference on Natural Computation, IEEE, Xiamen, China, DOI: 10.1109/ICNC.2014.697593, 2014.

[32] 
C. Friden, A. Hertz, and D. Werra, “Stabulus: A technique for finding stable sets in large graphs with tabu search,” Computing, vol.42, no.1, pp.35–44, 1989. doi: 10.1007/BF02243141

[33] 
F. Ma, J. K. Hao, and Y. Wang, “An effective iterated tabu search for the maximum bisection problem,” Computers & Operations Research, vol.81, pp.78–89, 2017.

[34] 
A. K. Jagota and K. W. Regan, “Performance of MAXCLIQUE Approximation heuristics under descriptionlength weighted distributions,” available at: http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=2FA485973535F33AA6535F861791FA33?doi=10.1.1.32.6486&rep=rep1&type=pdf, 1992.

[35] 
G. Yang and J. Yi, “Delayed chaotic neural network with annealing controlling for maximum clique problem,” Neurocomputing, vol.127, pp.114–123, 2014.

[36] 
Q. Ouyang, “DNA solution of the maximal clique problem,” Science, vol.278, no.5337, pp.446–449, 1997. doi: 10.1126/science.278.5337.446

[37] 
T. Head, G. Rozenberg, R. S. Bladergroen, et al., “Computing with DNA by operating on plasmids,” Biosystems, vol.57, no.2, pp.87–93, 2000. doi: 10.1016/S03032647(00)000915

[38] 
LI KenLi, ZHOU Xu, and ZOU ShuTing, “Improved volume molecular solutions for the maximum clique problem on DNAbased supercomputing,” Chinese Journal of Computers, vol.31, no.12, pp.2173–2181, 2008.

[39] 
Zhou Xu, Zhou Yantao, Ouyang Aijia, et.al, “An efficient tile assembly model for maximum clique problem,” Journal of Computer Research and Development, vol.51, no.6, pp.1253–1262, 2014.
