Max-flow min-cut theorem in an anisotropic network
type: Item
instance of: scholarly article
title: Max-flow min-cut theorem in an anisotropic network
zbMATH Open document ID: 0723.90020
author: Ryôhei Nozawa
published in: Osaka Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The author gives rigorous formulations of max-flow problems and min-cut problems on a bounded domain in the n-dimensional Euclidean space with Lipschitz boundary. The max-flow problems have anisotropic capacity constraints and contain continuous versions of max-flow problems of \textit{M. Iri} [in: Survey of mathematical programming, Proc. int. Symp., Vol. 2, Budapest 1976, 263-278 (1980; Zbl 0429.90029)] and \textit{G. Strang} [Math. Program. 26, 123-143 (1983; Zbl 0513.90026)]. According to Strang's idea the author takes an essentially bounded vector field as any flow and a subset of the domain such that the characteristic function is a function of bounded variation as any cut and proves that max-flow min- cut theorems for them hold if the capacity constraints satisfy some boundedness condition and continuity condition.
Mathematics Subject Classification ID: 90B10
Mathematics Subject Classification ID: 26B30
zbMATH DE Number: 4193424
zbMATH Keywords: max-flow
zbMATH Keywords: min-cut
zbMATH Keywords: Lipschitz boundary
zbMATH Keywords: anisotropic capacity constraints
MaRDI profile type: Publication
description: scientific article