Skip to main content
Top

2016 | OriginalPaper | Chapter

A Voltage-Mode Nonlinear-Synapse Neural Circuit for Bi-partitioning of Graphs

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

An NP-complete problem that finds applications in various fields in engineering and sciences is the graph partitioning problem. This paper presents a novel recurrent neural network, which makes use of nonlinearities in the feedback interconnections, for bipartitioning a given planar graph of n vertices (nodes). The scheme comprises of n neurons and n 2 synaptic interconnection weights, as compared to the n 2 neurons and n 4 synapses required by conventional Hopfield network approaches. PSPICE simulation results serve as verification for the proposed theory.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Arora, S., Rao, S., Vazirani, U.: Expander flows, geometric embeddings and graph partitioning. J. ACM, 56(5), 1–5:37 (2009) Arora, S., Rao, S., Vazirani, U.: Expander flows, geometric embeddings and graph partitioning. J. ACM, 56(5), 1–5:37 (2009)
2.
go back to reference Du, K.L.: Clustering: a neural network approach. Neural Networks 23(1), 89–107 (2010)CrossRef Du, K.L.: Clustering: a neural network approach. Neural Networks 23(1), 89–107 (2010)CrossRef
3.
go back to reference Mandala, S.R., Kumara, S.R.T., Rao, C.R., Albert, R.: Clustering social networks using ant colony optimization. Oper. Res. Int. J. 13(1), 47–65 (2013)CrossRef Mandala, S.R., Kumara, S.R.T., Rao, C.R., Albert, R.: Clustering social networks using ant colony optimization. Oper. Res. Int. J. 13(1), 47–65 (2013)CrossRef
4.
go back to reference Mitra, M., Carvunis, A.-R., Ramesh, S.K., Ideker, T.: Integrative approaches for finding modular structure in biological networks. Nat. Rev. Genet. 14(10), 719–732 (2013)CrossRef Mitra, M., Carvunis, A.-R., Ramesh, S.K., Ideker, T.: Integrative approaches for finding modular structure in biological networks. Nat. Rev. Genet. 14(10), 719–732 (2013)CrossRef
5.
go back to reference Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell Sys. Tech. J. 49(2), 291–307 (1970)CrossRefMATH Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell Sys. Tech. J. 49(2), 291–307 (1970)CrossRefMATH
6.
go back to reference Fiduccia, C.M., Mattheyses, R.M.: A linear-time heuristic for improving network partitions. J. ACM 175–181 (1982) Fiduccia, C.M., Mattheyses, R.M.: A linear-time heuristic for improving network partitions. J. ACM 175–181 (1982)
7.
go back to reference Talbi, E.-G., Bessiere, P.: A parallel genetic algorithm for the graph partitioning problem. In: Proceedings of 5th International Conference on Supercomputing, ICS’91, pp. 312–320. ACM, USA (1991) Talbi, E.-G., Bessiere, P.: A parallel genetic algorithm for the graph partitioning problem. In: Proceedings of 5th International Conference on Supercomputing, ICS’91, pp. 312–320. ACM, USA (1991)
8.
go back to reference Pain, C.C., De Oliveira, C.R.E., Goddard, A.J.H.: A neural network graph partitioning procedure for grid-based domain decomposition. Int. J. Num. Methods Eng. 44(5), 593–613 (1999)CrossRefMATH Pain, C.C., De Oliveira, C.R.E., Goddard, A.J.H.: A neural network graph partitioning procedure for grid-based domain decomposition. Int. J. Num. Methods Eng. 44(5), 593–613 (1999)CrossRefMATH
9.
go back to reference Yih J.-S. and Mazumder P. A neural network design for circuit partitioning. IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 9(12), 1265–1271 (1990) Yih J.-S. and Mazumder P. A neural network design for circuit partitioning. IEEE Trans. Comput.-Aided Des. Int. Cir. Sys. 9(12), 1265–1271 (1990)
10.
go back to reference Smith, K.A.: Neural networks for combinatorial optimization: a review of more than a decade of research. INFORMS J. Comput. 11(1), 15–34 (1999)MathSciNetCrossRefMATH Smith, K.A.: Neural networks for combinatorial optimization: a review of more than a decade of research. INFORMS J. Comput. 11(1), 15–34 (1999)MathSciNetCrossRefMATH
11.
go back to reference Ansari, M.S.: The graph coloring problem–review of algorithms & neural networks and a new proposal. In: International Conference on Multimedia, Signal Processing and Communication Technologies (IMPACT), pp. 310–314. India (2013) Ansari, M.S.: The graph coloring problem–review of algorithms & neural networks and a new proposal. In: International Conference on Multimedia, Signal Processing and Communication Technologies (IMPACT), pp. 310–314. India (2013)
12.
go back to reference Ansari, M.S., Non-Linear Feedback Neural Networks. Studies in Computational Intelligence, vol. 508. Springer (2013) Ansari, M.S., Non-Linear Feedback Neural Networks. Studies in Computational Intelligence, vol. 508. Springer (2013)
13.
go back to reference Jayadeva, Rahman S.A. A neural network with O(N) neurons for ranking N numbers in O(1/N) time. IEEE Tran. Circ. Sys. I: Regul. Pap. 51(10):2044–2051 (2004) Jayadeva, Rahman S.A. A neural network with O(N) neurons for ranking N numbers in O(1/N) time. IEEE Tran. Circ. Sys. I: Regul. Pap. 51(10):2044–2051 (2004)
14.
go back to reference Senani, R.: Realisation of linear voltage-controlled resistance in floating form. Electron. Lett. 30(23), 1909–1911 (1994)CrossRef Senani, R.: Realisation of linear voltage-controlled resistance in floating form. Electron. Lett. 30(23), 1909–1911 (1994)CrossRef
15.
go back to reference Ansari, M.S.: Employing differential voltage current conveyor in graph coloring applications. In: International Conference on Power, Control and Embedded Systems (ICPCES), pp. 1–3 (2010) Ansari, M.S.: Employing differential voltage current conveyor in graph coloring applications. In: International Conference on Power, Control and Embedded Systems (ICPCES), pp. 1–3 (2010)
16.
go back to reference Soper, A.J., Walshaw, C., Cross, M.: A combined evolutionary search and multilevel optimisation approach to graph-partitioning. J. Global Optim. 29(2), 225–241 (2004)MathSciNetCrossRefMATH Soper, A.J., Walshaw, C., Cross, M.: A combined evolutionary search and multilevel optimisation approach to graph-partitioning. J. Global Optim. 29(2), 225–241 (2004)MathSciNetCrossRefMATH
17.
go back to reference Verbelen, T., Stevens, T., De Turck, F., Dhoedt, B.: Graph partitioning algorithms for optimizing software deployment in mobile cloud computing. Future Gener. Comput. Syst. 29(2), 451–459 (2013)CrossRef Verbelen, T., Stevens, T., De Turck, F., Dhoedt, B.: Graph partitioning algorithms for optimizing software deployment in mobile cloud computing. Future Gener. Comput. Syst. 29(2), 451–459 (2013)CrossRef
18.
go back to reference Hager, W.W., Phan, D.T., Zhang, H.: An exact algorithm for graph partitioning. Math. Prog. 137(1-2), 531–556 (2013) Hager, W.W., Phan, D.T., Zhang, H.: An exact algorithm for graph partitioning. Math. Prog. 137(1-2), 531–556 (2013)
19.
go back to reference Mérida-Casermeiro, E., López-Rodríguez, D.: Graph partitioning via recurrent multivalued neural networks. In: Computational Intelligence and Bioinspired Systems, pp. 1149–1156. Springer (2005) Mérida-Casermeiro, E., López-Rodríguez, D.: Graph partitioning via recurrent multivalued neural networks. In: Computational Intelligence and Bioinspired Systems, pp. 1149–1156. Springer (2005)
Metadata
Title
A Voltage-Mode Nonlinear-Synapse Neural Circuit for Bi-partitioning of Graphs
Author
Mohd Samar Ansari
Copyright Year
2016
Publisher
Springer India
DOI
https://doi.org/10.1007/978-81-322-2638-3_17