Enhancements Of Spanning Tree Labelling Procedures For Network Optimization

Barr, Ronald E.; Glover, Fred; Klingman, Darwin

doi:10.1080/03155986.1979.11731713

Cited by 43 publications

(49 citation statements)

References 8 publications

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“…Quasi-tree after updating (special arc dotted). Ln the testing done in [2], inclusion of the reverse thread resulted in only a 5 percent reduction in solution times. It seems likely that this conclusion will carry over to generalized networks as well.…”

Section: Computational Considerationsmentioning

confidence: 99%

“…The node functions we use are those of Barr, Glover, and Klingman [2], and we adopt their notation whenever possible.…”

Section: Basis Structurementioning

confidence: 99%

“…In [2], the subtree with the smaller number of nodes is identified using t(x) values, and the node potentials are t-.…”

Section: Computational Considerationsmentioning

confidence: 99%

“…In this paper we present a method for implementing the primal simplex algorithm for generalized networks which builds on the labeling procedures used in one of the fastest pure network codes [2]. Our approach has the advantage of being quite easy to understand, and it should give rise to computer codes which are Ahighly efficient and easily maintained.…”

Section: Introductionmentioning

confidence: 99%

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New labeling procedures for the basis graph in generalized networks

Engquist

Chang

1985

Operations Research Letters

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Section: Computational Considerationsmentioning

confidence: 99%

“…The node functions we use are those of Barr, Glover, and Klingman [2], and we adopt their notation whenever possible.…”

Section: Basis Structurementioning

confidence: 99%

“…In [2], the subtree with the smaller number of nodes is identified using t(x) values, and the node potentials are t-.…”

Section: Computational Considerationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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New labeling procedures for the basis graph in generalized networks

Engquist

Chang

1985

Operations Research Letters

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“…Not only is it one of the fastest transportation codes in existence , it has the smalles t memory requirements of any known code for this problem . Specifically, only four node-length arrays and two arc-length arrays mus t be stored as opposed , for example , to four and eleven , respectively , for the SUPERK code [ 4] . These spacial parameters are exceptionally important in this context since additional fixed-charge values and the branch-and-bound tree structure require another five arc-length arrays.…”

Section: Algorithm For Trdnsportation Subproblemsmentioning

confidence: 99%

A New Optimization Method for Large Scale Fixed Charge Transportation Problems

Barr

Glover

Klingman

1981

Operations Research

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This paper presents a branch-and-bound algorithm for solving fixed charge transportation problems where not all cells exist. The algorithm exploits the absence of full problem density in several ways, thus yielding a procedure which is especially applicable to solving real world problems which are normally quite sparse. Additionally, streamlined new procedures for pruning the decision tree and calculating penalties are presented. We present computational experience with both a set of large test problems and a set of dense test problems from the literature. Comparisons with other codes are uniformly favorable to the new method, which runs more than twice as fast as the best alternative.

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Parallel network simplex algorithm for the minimum cost flow problem

Kara

Özturan

2021

Concurrency and Computation

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In 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. We propose finding the entering arc in parallel as it often takes the majority of the execution time. A usual strategy is to pick the arc violating the optimality the most out of all possible candidates. Scanning all arcs can take quite some time, so it is common to consider only a fixed number of arcs which is referred as the block search pivoting rule. Arc scans can easily be done in parallel to find the best candidate as the calculations are independent of each other. We used shared memory parallelism using OpenMP along with vectorization using AVX instructions. We also tried adjusting block sizes to increase the parallel portion of the algorithm.Our dataset consists of various natural and synthetic graphs with sizes up to a billion arc. Our experiments show speedups up to four are possible, though they are typically lower.

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Enhancements Of Spanning Tree Labelling Procedures For Network Optimization

Cited by 43 publications

References 8 publications

New labeling procedures for the basis graph in generalized networks

New labeling procedures for the basis graph in generalized networks

A New Optimization Method for Large Scale Fixed Charge Transportation Problems

Parallel network simplex algorithm for the minimum cost flow problem

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