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A Faster Primal Network Simplex Algorithm
1996We 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.
Aggarwal, Charu C. +2 more
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Network Simplex: The Fastest Algorithm
2022Hassan Rashidi, Edward P. K. Tsang
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Efficiency of the Primal Network Simplex Algorithm for the Minimum-Cost Circulation Problem
Mathematics of Operations Research, 1991We study the number of pivots required by the primal network simplex algorithm to solve the minimum-cost circulation problem. We propose a pivot selection rule with a bound of n(logn)/2+O(1) on the number of pivots, for an n-vertex network. This is the first known subexponential bound. The network simplex algorithm with this rule can be implemented to
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Parallel network simplex algorithm for the minimum cost flow problem
Concurrency Computation Practice and Experience, 2022Gokcehan Kara, Can Ozturan
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Network Simplex Plus: Complete Advanced Algorithm
2022Hassan Rashidi, Edward P. K. Tsang
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A Simplex-based simulated annealing algorithm for node-arc capacitated multicommodity network design
Applied Soft Computing Journal, 2012Masoud Yaghini
exaly
A polynomial time primal network simplex algorithm for minimum cost flows
Mathematical Programming, 1997James Orlin, Orlin James B
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