A Faster Primal Network Simplex Algorithm
Name
OR-315-95.pdf
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952.09 KB
Format
Adobe PDF
Checksum (MD5)
15306f72adaf1b2af4ca716a980c894e
Author(s)
Aggarwal, Charu C.
Kaplan, Haim
Tarjan, Robert E., 1948-
Date Issued
March 1996
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 315-96
Abstract
We present a faster implementation of the polynomial time primal simplex algorithm due to Orlin [23]. His algorithm requires O(nm min{log(nC), m log n}) pivots and O(n2 m ??n{log nC, m log n}) time. The bottleneck operations in his algorithm are performing the relabeling operations on nodes, selecting entering arcs for pivots, and performing the pivots. We show how to speed up these operations so as to yield an algorithm whose running time is O(nm. log n) per scaling phase. We show how to extend the dynamic-tree data-structure in order to implement these algorithms. The extension may possibly have other applications as well.
Subjects
Network Flows, Simplex algorithm, polynomial time, premultipliers.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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