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A Strongly Convergent Primal Simplex Algorithm for Generalized Networks
Mathematics of Operations Research, 1979A major computational problem that arises in the attempt to solve generalized network and network-related problems is degeneracy. In fact, using primal simplex solution techniques, the number of degenerate pivots performed frequently ranges as high as 90% in large-scale applications.
Joyce J. Elam +2 more
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A Network Simplex Algorithm for the Equal Flow Problem on a Generalized Network
INFORMS Journal on Computing, 2013A network simplex algorithm is described for the minimum-cost network flow problem on a generalized network, with the additional constraint that there exist sets of arcs that must carry equal amounts of flow. This problem can be modeled as a linear programming problem and solved using the standard simplex algorithm.
David R. Morrison +2 more
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Parallel network simplex algorithm for the minimum cost flow problem
Concurrency and Computation: Practice and Experience, 2021AbstractIn this work, we contribute a parallel implementation of the network simplex algorithm that is used for the solution of minimum cost flow problem. In the network simplex algorithm, finding an entering arc requires searching through many arcs to decide which one should be included in the spanning tree solution on the next iteration.
Gökçehan Kara, Can C. Özturan
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Implementing an LU Factorization for the Embedded Network Simplex Algorithm
INFORMS Journal on Computing, 2004This paper presents an LU factorization specialized for embedded network simplex algorithms. Specializing the LU factorization in this fashion poses a challenge as the embedded network algorithm uses a very compressed working basis inverse. Using publicly available test problems, we demonstrate the impact of this factorization on the EMNET ...
Richard D. McBride, John W. Mamer
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Anti‐stalling pivot rules for the network simplex algorithm
Networks, 1990AbstractStalling in the simplex algorithm is defined as an exponentially long sequence of consecutive degenerate pivots without cycling. Pivot rules for the network simplex algorithm that prevent both cycling and stalling are considered. For several of these, the number of consecutive degenerate pivots is shown to be at most k (k + 1)/2, where k is the
Donald Goldfarb +2 more
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A new pivot selection rule for the network simplex algorithm
Mathematical Programming, 1997We present a new network simplex pivot selection rule, which we call the minimum ratio pivot rule, and analyze the worst-case complexity of the resulting network simplex algorithm. We consider networks with n nodes, m arcs, integral arc capacities and integral supplies/demands of nodes. We define a {0, 1}-valued penalty for each arc of the network. The
Sokkalingam, P. T. +2 more
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2013
For practical applications, by far the most useful optimization algorithm for solving linear programs is the celebrated simplex algorithm. This suggests trying to apply this algorithm also to problems from graph theory. Indeed, the most important network optimization problems may be formulated in terms of linear programs; this holds, for instance, for ...
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For practical applications, by far the most useful optimization algorithm for solving linear programs is the celebrated simplex algorithm. This suggests trying to apply this algorithm also to problems from graph theory. Indeed, the most important network optimization problems may be formulated in terms of linear programs; this holds, for instance, for ...
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An efficient generalized network-simplex-based algorithm for manufacturing network flows
Journal of Combinatorial Optimization, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Prahalad Venkateshan +2 more
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An exterior simplex type algorithm for the Minimum Cost Network Flow Problem
Computers & Operations Research, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Konstantinos Paparrizos +2 more
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A Subtree-Partitioning Algorithm for Inducing Parallelism in Network Simplex Dual Updates
Computational Optimization and Applications, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Betty L. Hickman, Dan Scott
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