A neural network parallel algorithm for Ramsey numbers

K. Tsuchiya, Yoshiyasu Takefuji

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A neural network parallel algorithm for finding Ramsey numbers in two-coloring is described. The Ramsey number R(r,b) is given by the smallest value of N, where all edges of a complete graph of (N-1) vertices are colored either red or blue, and red-colored and blue-colored subgraphs should not form any complete subgraph of r vertices and b vertices, respectively. A superimposed red-colored and blue-colored subgraph is called a Ramsey graph. The parallel algorithm, which is based on the hysteresis McCulloch-Pitts neural network, found five Ramsey numbers successfully. The neural network requires n(n-1) neurons for a Ramsey number of an n-vertex complete graph. The simulation result for the algorithm is so promising that it may be possible to find unknown Ramsey numbers.

Original languageEnglish
Title of host publicationProceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1166-1171
Number of pages6
ISBN (Electronic)0780308093, 9780780308091
DOIs
Publication statusPublished - 1992 Jan 1
Externally publishedYes
Event1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992 - Rostov-on-Don, Russian Federation
Duration: 1992 Oct 71992 Oct 10

Publication series

NameProceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992

Conference

Conference1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992
CountryRussian Federation
CityRostov-on-Don
Period92/10/792/10/10

Fingerprint

Parallel algorithms
Neural networks
Coloring
Neurons
Hysteresis

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Science Applications
  • Information Systems

Cite this

Tsuchiya, K., & Takefuji, Y. (1992). A neural network parallel algorithm for Ramsey numbers. In Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992 (pp. 1166-1171). [268617] (Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/RNNS.1992.268617

A neural network parallel algorithm for Ramsey numbers. / Tsuchiya, K.; Takefuji, Yoshiyasu.

Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992. Institute of Electrical and Electronics Engineers Inc., 1992. p. 1166-1171 268617 (Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Tsuchiya, K & Takefuji, Y 1992, A neural network parallel algorithm for Ramsey numbers. in Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992., 268617, Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992, Institute of Electrical and Electronics Engineers Inc., pp. 1166-1171, 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992, Rostov-on-Don, Russian Federation, 92/10/7. https://doi.org/10.1109/RNNS.1992.268617
Tsuchiya K, Takefuji Y. A neural network parallel algorithm for Ramsey numbers. In Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992. Institute of Electrical and Electronics Engineers Inc. 1992. p. 1166-1171. 268617. (Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992). https://doi.org/10.1109/RNNS.1992.268617
Tsuchiya, K. ; Takefuji, Yoshiyasu. / A neural network parallel algorithm for Ramsey numbers. Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992. Institute of Electrical and Electronics Engineers Inc., 1992. pp. 1166-1171 (Proceedings 1992 RNNS/IEEE Symposium on Neuroinformatics and Neurocomputers, RNNS 1992).
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