Maximum-Flow Neural Network: A Novel Neural Network for the Maximum Flow Problem

Sato, Masatoshi; Aomori, Hisashi; Tanaka, Mamoru

doi:10.1587/transfun.e92.a.945

Cited by 5 publications

(8 citation statements)

References 8 publications

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“…The dynamical behavior of the circuit is described by a set of nonlinear differential equations. It was observed through a number of computer simulations that the circuit always converges to an equilibrium point that corresponds to the maximum flow [16]. We thus expect that this property can be proved rigorously.…”

Section: Introductionmentioning

confidence: 78%

“…In addition to the above-mentioned work, various recurrent neural network models for optimization problems have been investigated in the literature (see e.g., [11,12] and references therein). Also, some authors proposed to use SPICE, the most widely used circuit simulator, for solving constrained optimization problems [13][14][15] Recently, Sato et al [16] proposed a class of nonlinear circuits 1 for solving maximum flow problems. A maximum flow problem is the problem to find the maximum amount of flow from the source to the sink through capacitated edges in a given network.…”

Section: Introductionmentioning

confidence: 99%

“…However, unfortunately, the stability or the convergence of the circuit has not been completely understood so far. It was claimed in [16] that the circuit always converges to an equilibrium point, but the proof there is far from complete.…”

Section: Introductionmentioning

confidence: 99%

“…Since the maximum flow problem is formulated as a linear programming problem [19], all nonlinear circuits that can solve linear programming problems can be applied to the maximum flow problem. However, those circuits have in general a more complicated structure than the one proposed by Sato et al [16] that is specialized to the maximum flow problem. On the other hand, a nonlinear circuit model proposed by Dennis [1] has a simple structure.…”

Section: Introductionmentioning

confidence: 99%

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Global asymptotic stability of nonlinear circuits related to maximum flow problems

Takahashi

2011

NOLTA

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Global asymptotic stability of the nonlinear circuit similar to the one proposed by Sato et al. for solving the maximum flow problem is studied in this paper. The circuit consists of two independent DC voltage sources, capacitors and nonlinear resistors. It is proved rigorously that the circuit has a unique equilibrium point which is globally asymptotically stable. From the viewpoint of dynamical systems, the circuit is a cooperative system, and thus some fundamental results concerning the convergence property of cooperative systems play important roles.

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Section: Introductionmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global asymptotic stability of nonlinear circuits related to maximum flow problems

Takahashi

2011

NOLTA

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“…The important point is that our proposed method enables the simultaneous analysis only by nonlinear resistive circuit analysis. In our previous research, we have proposed the Maximum-Flow Neural Network (MF-NN), which is a novel max-flow algorithm based on the nonlinear resistive circuit analysis [13,14]. We have also showed that the analysis of the max-flow by the MF-NN boils down to the analysis of current distribution on the nonlinear resistive circuit.…”

Section: Introductionmentioning

confidence: 99%

Potential method of nonlinear resistive circuits to solve max-flow/min-cut problems

Sato

Aomori

Otake

et al. 2016

NOLTA

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Abstract:In this paper, we propose a new potential method of nonlinear resistive circuits to solve the max-flow/min-cut problems. The important point is that simultaneous analysis of the max-flow and the min-cut can be made based on the dynamics of a single state in the circuit. Although the max-flow problem and the min-cut problem are in duality, the respective algorithms are different in conventional methods. In other words, the simultaneous analysis for the max-flow/min-cut problems does not exist. Our proposed method enables the simultaneous analysis only by nonlinear resistive circuit analysis. Additionally, the min-cut can be found from the node voltages directly. The node voltages enable the finding of all min-cuts easily when a graph has multiple min-cuts, which are found when plural cuts with the same min-cut capacity exist in the same graph. In conventional min-cut algorithms, it is hard to obtain multiple min-cuts. Moreover, our proposed method has a huge advantage of being suitable for hardware implementation. When the proposed circuit model is designed with the integrated circuit such as analog type Programmable Logic Device, Memristor or Phase Change Memory which can change graph structure and branch conductance, the novel min-cut solution with real-time processing can be expected.

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Image Segmentation Using Graph Cuts Based on Maximum-Flow Neural Network

Sato

Toda

Aomori

et al. 2016

Neural Information Processing

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Maximum-Flow Neural Network: A Novel Neural Network for the Maximum Flow Problem

Cited by 5 publications

References 8 publications

Global asymptotic stability of nonlinear circuits related to maximum flow problems

Global asymptotic stability of nonlinear circuits related to maximum flow problems

Potential method of nonlinear resistive circuits to solve max-flow/min-cut problems

Image Segmentation Using Graph Cuts Based on Maximum-Flow Neural Network

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