The relax codes for linear minimum cost network flow problems

We describe a relaxation algorithm [1,2] for solving the classical minimum cost network flow problem. Our implementation is compared with mature state-of-the-art primal simplex and primal-dual codes and is found to be several times faster on all types of randomly generated network flow problems. Furthermore, the speed-up factor increases with problem dimension. The codes, called RELAX-II and RELAXT-II, have a facility for efficient reoptimization and sensitivity analysis, and are in the public domain.

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