Efficient Parallel Algorithms for the Minimum Cost Flow Problem

In this paper, we propose efficient parallel implementations of the auction/sequential shortest path and the ∈-relaxation algorithms for solving the linear minimum cost flow problem. In the parallel auction algorithm, several augmenting paths can be found simultaneously, each of them starting from a...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 95; no. 3; pp. 501 - 530
Main Authors: Beraldi, P., Guerriero, F., Musmanno, R.
Format: Journal Article
Language:English
Published: New York, NY Springer 01.12.1997
Springer Nature B.V
Subjects:
Algorithms
Applied sciences
Exact sciences and technology
Flows in networks. Combinatorial problems
Operational research and scientific management
Operational research. Management science
Multiprocessor
Cost minimization
Parallel algorithm
Network flow
Shortest path
Relaxation method
Graph theory
Shared memory
Optimization
Convergence
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:In this paper, we propose efficient parallel implementations of the auction/sequential shortest path and the ∈-relaxation algorithms for solving the linear minimum cost flow problem. In the parallel auction algorithm, several augmenting paths can be found simultaneously, each of them starting from a different node with positive surplus. Convergence results of an asynchronous version of the algorithm are also given. For the ∈-relaxation method, there exist already parallel versions implemented on CM-5 and CM-2; our implementation is the first on a shared memory multiprocessor. We have obtained significant speedup values for the algorithms considered; it turns out that our implementations are effective and efficient.
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ISSN:0022-3239
1573-2878
DOI:10.1023/A:1022613603828