A Parallel Asynchronous Implementation of the e-Relaxation Method for the Linear Minimum Cost Flow Problem

Abstract In this paper we present a parallel asynchronous implementation of the ϵ-relaxation method for solving the linear minimum cost flow problem on distributed memory message-passing multiprocessor systems. The general structure of the method is well suited to efficient parallelization, since a single iteration can be performed on several nodes simultaneously. We describe the implementation details of the parallel version on both a Fujitsu AP1000 and a cluster of Digital Alpha workstations connected via FDDI links. The results obtained demonstrate that our implementation is capable of substantial speedups.

[1]  Donald L. Miller,et al.  Solution of large dense transportation problems using a parallel primal algorithm , 1990 .

[2]  Andrew V. Goldberg,et al.  Finding Minimum-Cost Circulations by Successive Approximation , 1990, Math. Oper. Res..

[3]  Devendra Kumar,et al.  Development of a Class of Distributed Termination Detection Algorithms , 1992, IEEE Trans. Knowl. Data Eng..

[4]  Dimitri P. Bertsekas,et al.  Parallel primal-dual methods for the minimum cost flow problem , 1993, Comput. Optim. Appl..

[5]  Richard S. Barr,et al.  Parallel Simplex for Large Pure Network Problems: Computational Testing and Sources of Speedup , 1994, Oper. Res..

[6]  Darwin Klingman,et al.  NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems , 1974 .

[7]  George Karypis,et al.  Introduction to Parallel Computing , 1994 .

[8]  Andrew V. Goldberg,et al.  Solving minimum-cost flow problems by successive approximation , 1987, STOC.

[9]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[10]  D. R. Fulkerson,et al.  A primal‐dual algorithm for the capacitated Hitchcock problem , 1957 .

[11]  Xiaoye S. Li,et al.  Data-level parallel solution of min-cost network flow problems using ϵ-relaxations , 1994 .

[12]  Panos M. Pardalos,et al.  Advances in Optimization and Parallel Computing , 1992 .

[13]  Andrew Vladislav Goldberg,et al.  Efficient graph algorithms for sequential and parallel computers , 1987 .