Computational Experience with a Parallel Implementation of an Interior-Point Algorithm for Multicommodity Network Flows

A parallel implementation of the specialized interior-point algorithm for multicommodity network flows introduced in [5] is presented. In this algorithm, the positive definite systems of each iteration are solved through a scheme that combines direct factorization and a preconditioned conjugate gradient (PCG) method. Since the solution of at least k independent linear systems is required at each iteration of the PCG, k being the number of commodities, a coarse-grained parallellization of the algorithm naturally arises. Also, several other minor steps of the algorithm are easily parallelized by commodity. An extensive set of computational results on a shared memory machine is presented, using problems of up to 2.5 million variables and 260,000 constraints. The results show that the approach is especially competitive on large, difficult multicommodity flow problems.

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