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Efficient Parallel Algorithms for the Minimum Cost Flow Problem

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Abstract

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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Authors and Affiliations

  1. Dipartimento di Elettronica, Informatica e Sistemistica, Università della Calabria, Rende, Cosenza, Italy

    P. Beraldi (Research Assistant) & F. Guerriero

  2. Dipartimento di Elettronica, Informatica e Sistemistica, Università della Calabria, Rende, Cosenza, Italy

    R. Musmanno (Assistant Professor)

Authors
  1. P. Beraldi
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  2. F. Guerriero
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  3. R. Musmanno
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Beraldi, P., Guerriero, F. & Musmanno, R. Efficient Parallel Algorithms for the Minimum Cost Flow Problem. Journal of Optimization Theory and Applications 95, 501–530 (1997). https://doi.org/10.1023/A:1022613603828

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