Polynomial dual network simplex algorithms PDF
Preview Polynomial dual network simplex algorithms
cUtWiiV HD28 .M414 WORKING PAPER ALFRED SLOAN SCHOOL OF MANAGEMENT P. Polynomial Dual Network Simplex Algorithms James B. Orlin, Serge A. Plotkin and Eva Tardos WP# 3333-91-MSA September, 1991 MASSACHUSETTS INSTITUTE OF TECHNOLOGY 50 MEMORIAL DRIVE CAMBRIDGE, MASSACHUSETTS 02139 Polynomial Dual Network Simplex Algorithms James B. Orlin, Serge A. Plotkin and Eva Tardos WP# 3333-91-MSA September, 1991 / Polynomial Dual Network Simplex Algorithms James B. Orlin* Sloan School of Management Science MIT Serge A. Plotkin^ Department of Computer Science, Stanford University Eva Tardo^ School of Operations Research, Cornell University Abstract We show how to use polynomial and strongly polynomial capacity seeding algorithms for the transshipment problem to design a polynomial dual network simplex pivot rule. Our best pivoting strategy leads to an 0(m^logn) bound on the number ofpivots, where n and m denotes the number of nodes and arcs in the input network. If the demands are integral and at most B, we also give an C'(m(m+nlogn)min(logn5,mlogn))-time implementation ofa strategy that requires somewhat more pivots. •Research supported by AFOSR-88-0088 through the Air Force Office of Scientific Research, by NSF grant DDM-8921835 and by grants from Prime Computer Corporation and UPS. 'Research supported by NSF Research Initiation Award CCR-900-8226 and by ONR Contract N00014-88- K-0166. 'Research supported in part a David and Lucile Packard 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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