Abstract
We show how to use polynomial and strongly polynomial capacity scaling algorithms for the transshipment problem to design a polynomial dual network simplex pivot rule. Our best pivoting strategy leads to an O(m 2 logn) bound on the number of pivots, wheren andm denotes the number of nodes and arcs in the input network. If the demands are integral and at mostB, we also give an O(m(m+n logn) min(lognB, m logn))-time implementation of a strategy that requires somewhat more pivots.
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Research supported by AFOSR-88-0088 through the Air Force Office of Scientific Research, by NSF grant DOM-8921835 and by grants from Prime Computer Corporation and UPS.
Research supported by NSF Research Initiation Award CCR-900-8226, by U.S. Army Research Office Grant DAAL-03-91-G-0102, and by ONR Contract N00014-88-K-0166.
Research supported in part by a Packard Fellowship, an NSF PYI award, a Sloan Fellowship, and by the National Science Foundation, the Air Force Office of Scientific Research, and the Office of Naval Research, through NSF grant DMS-8920550.
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Orlin, J.B., Plotkin, S.A. & Tardos, É. Polynomial dual network simplex algorithms. Mathematical Programming 60, 255–276 (1993). https://doi.org/10.1007/BF01580615
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DOI: https://doi.org/10.1007/BF01580615