Unimodular matrices of flow problems with additional constraints
- 1 December 1977
- Vol. 7 (4) , 343-358
- https://doi.org/10.1002/net.3230070406
Abstract
A graph‐theoretic characterization of unimodular matrices arising from flow problems with additional constraints is developed. The resulting necessary and sufficient conditions are utilized to determine the class of unimodular matrices of multicommodity transportation problems.Keywords
This publication has 13 references indexed in Scilit:
- An efficient scaling procedure for gain networksNetworks, 1976
- Finding equivalent transportation formulations for constrained transportation problemsNaval Research Logistics Quarterly, 1974
- Total unimodularity and the transportation problem: a generalizationLinear Algebra and its Applications, 1974
- Two commodity network flows and linear programmingMathematical Programming, 1973
- Integral Extreme PointsSIAM Review, 1968
- Letter to the Editor—A Constrained Shortest Route ProblemOperations Research, 1968
- Generalized upper bounding techniquesJournal of Computer and System Sciences, 1967
- Characterization of totally unimodular matricesProceedings of the American Mathematical Society, 1965
- On unimodular matricesPacific Journal of Mathematics, 1962
- On linear systems with integral valued solutionsPacific Journal of Mathematics, 1957