Abstract
Signature algorithms solve certain classes of transportation problems in a number of steps bounded by the diameter of the dual polyhedron. The class of problems to which signature algorithms may be applied—the “signature classes” of the title—are characterized, and the monotonic Hirsch conjecture is shown to hold for them. In addition, certain more precise results are given for different cases. Finally, it is explained why a supposed proof of the Hirsch conjecture for all transportation polytopes is incomplete and apparently irremedial.
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Dedicated with affection to Philip Wolfe on the occasion of his 65th birthday.
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Balinski, M.L., Rispoli, F.J. Signature classes of transportation polytopes. Mathematical Programming 60, 127–144 (1993). https://doi.org/10.1007/BF01580606
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DOI: https://doi.org/10.1007/BF01580606