### Abstract

Two new approaches called 'graph unitization' are proposed to apply neural networks similar to the Hopfield-Tank models to determine optimal solutions for the maximum flow problem. They are: (1) n-vertex and n^{2}-edge neurons on a unitized graph; (2) m-edge neurons on a unitized graph. Graph unitization is to make the flow capacity of every edge equal to 1 by placing additional vertices or edges between existing vertices. In our experiments, solutions converged most of the time, and the converged solutions were always optimal, rather than near optimal.

Original language | English |
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Pages (from-to) | 174-177 |

Number of pages | 4 |

Journal | IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications |

Volume | 41 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1994 Feb |

Externally published | Yes |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications*,

*41*(2), 174-177. https://doi.org/10.1109/81.269056

**Modified Hopfield-Tank neural networks applied to the 'unitized' maximum flow problem.** / Munakata, Toshinori; Takefuji, Yoshiyasu; Johansson, Henrik.

Research output: Contribution to journal › Article

*IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications*, vol. 41, no. 2, pp. 174-177. https://doi.org/10.1109/81.269056

}

TY - JOUR

T1 - Modified Hopfield-Tank neural networks applied to the 'unitized' maximum flow problem

AU - Munakata, Toshinori

AU - Takefuji, Yoshiyasu

AU - Johansson, Henrik

PY - 1994/2

Y1 - 1994/2

N2 - Two new approaches called 'graph unitization' are proposed to apply neural networks similar to the Hopfield-Tank models to determine optimal solutions for the maximum flow problem. They are: (1) n-vertex and n2-edge neurons on a unitized graph; (2) m-edge neurons on a unitized graph. Graph unitization is to make the flow capacity of every edge equal to 1 by placing additional vertices or edges between existing vertices. In our experiments, solutions converged most of the time, and the converged solutions were always optimal, rather than near optimal.

AB - Two new approaches called 'graph unitization' are proposed to apply neural networks similar to the Hopfield-Tank models to determine optimal solutions for the maximum flow problem. They are: (1) n-vertex and n2-edge neurons on a unitized graph; (2) m-edge neurons on a unitized graph. Graph unitization is to make the flow capacity of every edge equal to 1 by placing additional vertices or edges between existing vertices. In our experiments, solutions converged most of the time, and the converged solutions were always optimal, rather than near optimal.

UR - http://www.scopus.com/inward/record.url?scp=0028375512&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028375512&partnerID=8YFLogxK

U2 - 10.1109/81.269056

DO - 10.1109/81.269056

M3 - Article

AN - SCOPUS:0028375512

VL - 41

SP - 174

EP - 177

JO - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

JF - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

SN - 1549-8328

IS - 2

ER -