Polynomial dual network simplex algorithms

40 Pages·1991·1.7 MB·English

by  Orlin, James B., 1953-

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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.