An efficient implementation of a network interior point method

Mauricio G.C. Resende and Geraldo Veiga

Extended version of published paper published in Network Flows and Matching: First DIMACS Implementation Challenge, D.S. Johnson and C.C. McGeoch, Eds., DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 12, pp. 299-348, 1993


We describe DLNET, an implementation of the dual affine scaling algorithm for minimum cost capacitated network flow problems.  The efficiency of this implementation is the result of three factors:  the small number of iterations taken by interior point methods, efficient solution of the linear system that determines the ascent direction using a preconditioned conjugate gradient algorithm and strategies to produce an optimal primal vertex solution.  The combination of these ingredients results in a code that can solve minimum cost network flow problems having hundreds of thousands of vertices in a few hours of running time on a workstation.  We compare DLNET with network simplex code NETFLO and relaxation code RELAXT-3 on an extensive range of minimum cost network flow problems, including minimum cost circulation, maximum flow and transshipment problems.

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