An Out-of-Kilter Method for Minimal-Cost Flow Problems

Previous article Next article An Out-of-Kilter Method for Minimal-Cost Flow ProblemsD. R. FulkersonD. R. Fulkersonhttps://doi.org/10.1137/0109002PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 Frank L. Hitchcock, The distribution of a product from several sources to numerous localities, J. Math. Phys. Mass. Inst. Tech., 20 (1941), 224–230 MR0004469 0026.33904 Google Scholar2 L. Kantorovitch, On the translocation of masses, C. R. (Doklady) Acad. Sci. URSS (N.S.), 37 (1942), 199–201 MR0009619 0061.09705 Google Scholar3 Tjalling C. Koopmans and , Stanley Reiter, A model of transportationActivity Analysis of Production and Allocation, Cowles Commission Monograph No. 13, John Wiley & Sons Inc., New York, N. Y., 1951, 222–259 MR0052757 0045.09704 Google Scholar4 George B. Dantzig, Application of the simplex method to a transportation problemActivity Analysis of Production and Allocation, Cowles Commission Monograph No. 13, John Wiley & Sons Inc., New York, N. Y., 1951, 359–373 MR0056262 0045.09901 Google Scholar5 H. W. Kuhn, The Hungarian method for the assignment problem, Naval Res. Logist. Quart., 2 (1955), 83–97 MR0075510 0143.41905 CrossrefGoogle Scholar6 H. W. Kuhn, Variants of the Hungarian method for assignment problems, Naval Res. Logist. Quart., 3 (1956), 253–258 (1957) MR0091857 0143.42001 CrossrefGoogle Scholar7 L. R. Ford, Jr. and , D. R. Fulkerson, Maximal flow through a network, Canad. J. Math., 8 (1956), 399–404 MR0079251 0073.40203 CrossrefGoogle Scholar8 L. R. Ford, Jr. and , D. R. Fulkerson, A simple algorithm for finding maximal network flows and an application to the Hitchcock problem, Canad. J. Math., 9 (1957), 210–218 MR0093427 0088.12907 CrossrefGoogle Scholar9 L. R. Ford, Jr. and , D. R. Fulkerson, Constructing maximal dynamic flows from static flows, Operations Res., 6 (1958), 419–433 MR0094894 CrossrefISIGoogle Scholar10 James Munkres, Algorithms for the assignment and transportation problems, J. Soc. Indust. Appl. Math., 5 (1957), 32–38 10.1137/0105003 MR0093429 0131.36604 LinkISIGoogle Scholar11 David Gale, A theorem on flows in networks, Pacific J. Math., 7 (1957), 1073–1082 MR0091855 0087.16303 CrossrefGoogle Scholar12 Alan J. Hoffman, Some recent applications of the theory of linear inequalities to extremal combinatorial analysisProc. Sympos. Appl. Math., Vol. 10, American Mathematical Society, Providence, R.I., 1960, 113–127 MR0114759 0096.00606 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Smoothed Analysis of the Successive Shortest Path AlgorithmTobias Brunsch, Kamiel Cornelissen, Bodo Manthey, Heiko Röglin, and Clemens Rösner10 December 2015 | SIAM Journal on Computing, Vol. 44, No. 6AbstractPDF (548 KB)Spirality and Optimal Orthogonal DrawingsGiuseppe Di Battista, Giuseppe Liotta, and Francesco Vargiu28 July 2006 | SIAM Journal on Computing, Vol. 27, No. 6AbstractPDF (645 KB)On Embedding a Graph in the Grid with the Minimum Number of BendsRoberto Tamassia13 July 2006 | SIAM Journal on Computing, Vol. 16, No. 3AbstractPDF (2032 KB)On Max Flows with Gains and Pure Min-Cost FlowsK. Truemper12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 32, No. 2AbstractPDF (699 KB) Volume 9, Issue 1| 1961Journal of the Society for Industrial and Applied Mathematics History Submitted:15 February 1960Published online:10 July 2006 InformationCopyright © 1961 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0109002Article page range:pp. 18-27ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics