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  1. Japan Journal of Industrial and Applied Mathematics
  2. Japan Journal of Industrial and Applied Mathematics : Volume 30
  3. Japan Journal of Industrial and Applied Mathematics : Volume 30, Issue 1, February 2013
  4. Universal Gröbner basis associated with the maximum flow problem
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Japan Journal of Industrial and Applied Mathematics : Volume 34
Japan Journal of Industrial and Applied Mathematics : Volume 33
Japan Journal of Industrial and Applied Mathematics : Volume 32
Japan Journal of Industrial and Applied Mathematics : Volume 31
Japan Journal of Industrial and Applied Mathematics : Volume 30
Japan Journal of Industrial and Applied Mathematics : Volume 30, Issue 3, November 2013
Japan Journal of Industrial and Applied Mathematics : Volume 30, Issue 2, June 2013
Japan Journal of Industrial and Applied Mathematics : Volume 30, Issue 1, February 2013
Metrics based on average distance between sets
Direct computation for American put option and free boundary using finite difference method
Universal Gröbner basis associated with the maximum flow problem
On traveling wave solutions to a Hamilton–Jacobi–Bellman equation with inequality constraints
Dynamics and interactions of spikes on smoothly curved boundaries for reaction–diffusion systems in 2D
L $^{2}$-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations
Weak interaction between zonal jets on a β plane
A refined Arnoldi type method for large scale eigenvalue problems
A planar convex domain with many isolated “ hot spots” on the boundary
Traveling waves of a nonlocal dispersal delayed age-structured population model
Combined adaptive meshing technique and finite volume element method for solving convection–diffusion equation
Quasi-chaotic behaviors of narrow-band response of a non-deterministic resonant system: application to analysis of ship motion in irregular seas
On a finite element approximation of the Stokes equations under a slip boundary condition of the friction type
Japan Journal of Industrial and Applied Mathematics : Volume 29
Japan Journal of Industrial and Applied Mathematics : Volume 28
Japan Journal of Industrial and Applied Mathematics : Volume 27
Japan Journal of Industrial and Applied Mathematics : Volume 26
Japan Journal of Industrial and Applied Mathematics : Volume 25
Japan Journal of Industrial and Applied Mathematics : Volume 24
Japan Journal of Industrial and Applied Mathematics : Volume 23
Japan Journal of Industrial and Applied Mathematics : Volume 22
Japan Journal of Industrial and Applied Mathematics : Volume 21
Japan Journal of Industrial and Applied Mathematics : Volume 20
Japan Journal of Industrial and Applied Mathematics : Volume 19
Japan Journal of Industrial and Applied Mathematics : Volume 18
Japan Journal of Industrial and Applied Mathematics : Volume 17
Japan Journal of Industrial and Applied Mathematics : Volume 16
Japan Journal of Industrial and Applied Mathematics : Volume 15
Japan Journal of Industrial and Applied Mathematics : Volume 14

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Universal Gröbner basis associated with the maximum flow problem

Content Provider Springer Nature Link
Author Watanabe, Sennosuke Watanabe, Yoshihide Ikegami, Daisuke
Copyright Year 2012
Abstract We give a formulation of the maximum flow problem as an integer programming problem in the standard form. We characterize elementary vectors of the kernel lattice of the matrix coefficient in our formulation in terms of the combinatorial property of the graph, such as circuits and s–t paths, and we determine the universal Gröbner basis of the toric ideal associated with the maximum flow problem. Next, we examine the kernel lattice of the reduced incidence matrix of the digraph. Under suitable assumptions for the digraph, we prove that it is generated by all incidence vectors of s–t directed paths, which yield the generator of the toric ideal associated with the reduced incidence matrix of the digraph.
Starting Page 39
Ending Page 50
Page Count 12
File Format PDF
ISSN 09167005
Journal Japan Journal of Industrial and Applied Mathematics
Volume Number 30
Issue Number 1
e-ISSN 1868937X
Language English
Publisher Springer Japan
Publisher Date 2012-06-22
Publisher Place Japan
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Maximum flow problem Circuit Universal Gröbner basis Flows in graphs Combinatorial aspects of simplicial complexes Programming involving graphs or networks Applications of Mathematics Computational Mathematics and Numerical Analysis
Content Type Text
Resource Type Article
Subject Applied Mathematics Engineering
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