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A bad network problem for the simplex method and other minimum cost flow algorithms
 Norman Zadeh
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For any integern, a modified transportation problem with 2n + 2 nodes is constructed which requires 2^{ n } + 2^{ n−2}−2 iterations using all but one of the most commonly used minimum cost flow algorithms.
As a result, the Edmonds—Karp Scaling Method [3] becomes the only known “good” (in the sense of Edmonds) algorithm for computing minimum cost flows.
 Busacker, R.G., Gowen, P.J. (1961) A procedure for determining a family of minimalcost network flow patterns. Operations Research Office, The Johns Hopkins University, Baltimore, Md.
 Dantzig, G.B. (1962) Linear programming and extensions. Princeton University Press, Princeton, N.J.
 Edmonds, J., Karp, R.M. (1972) Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the Association for Computing Machinery 19: pp. 248264
 Ford, L., Fulkerson, D.R. (1957) A primal dual algorithm for the capacitated Hitchcock problem. Naval Research Logistics Quarterly 4: pp. 4754
 Ford, L., Fulkerson, D.R. (1962) flows in networks. Princeton University Press, Princeton, N.J.
 Hu, T.C. (1969) Integer programming and network flows. AddisonWesley, Reading, Mass.
 V.L. Klee and G.J. Minty, “How good is the simplex algorithm”, Boeing Math. Note No. 643 (February 1970).
 Klein, M. (1967) A primal method for minimal cost flows. Management Science 14: pp. 205220
 Tomizawa, N. (1972) On some techniques useful for solution of transportation network problems. Networks 1: pp. 173194
 Wagner, H.M. (1959) On a class of capacitated transportation problems. Management Science 5: pp. 304318
 Zadeh, N. (1972) Theoretical efficiency of the Edmonds—Karp algorithm for computing maximal flows. Journal of the Association for Computing Machinery 19: pp. 184192
 Zadeh, N. (1972) Theoretical efficiency and partial equivalence of minimum cost flow algorithms: A bad network problem for the simplex method. Operations Research Center, University of California, Berkeley, Calif.
 Zadeh, N. (1973) More pathological examples for network flow problems. Mathematical programming 5: pp. 217224
 Title
 A bad network problem for the simplex method and other minimum cost flow algorithms
 Journal

Mathematical Programming
Volume 5, Issue 1 , pp 255266
 Cover Date
 19731201
 DOI
 10.1007/BF01580132
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
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 Authors

 Norman Zadeh ^{(1)}
 Author Affiliations

 1. IBM Thomas J. Watson Research Center, Yorktown Heights, New York, USA