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• W2091720300 abstract "We 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 (log n )/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 run in n (log n )/2+ O (1) time. In the special case of planar graphs, we obtain a polynomial bound on the number of pivots and the running time. We also consider the relaxation of the network simplex algorithm in which cost-increasing pivots are allowed as well as cost-decreasing ones. For this algorithm we propose a pivot selection rule with a bound of O(nm · min{log(nC), m log n}) on the number of pivots, for a network with n vertices, m arcs, and integer arc costs bounded in magnitude by C. The total running time is O(nm log n · min{(log nC), m log n}). This bound is within a logarithmic factor of those of the best previously known algorithms for the minimum-cost circulation problem." @default.
• W2091720300 created "2016-06-24" @default.
• W2091720300 creator A5051027549 @default.
• W2091720300 date "1991-05-01" @default.
• W2091720300 modified "2023-10-17" @default.
• W2091720300 title "Efficiency of the Primal Network Simplex Algorithm for the Minimum-Cost Circulation Problem" @default.
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• W2091720300 doi "https://doi.org/10.1287/moor.16.2.272" @default.
• W2091720300 hasPublicationYear "1991" @default.
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