@article{Gabow1989FasterSA,
title={Faster Scaling Algorithms for Network Problems},
author={Harold N. Gabow and Robert E. Tarjan},
journal={SIAM J. Comput.},
year={1989},
volume={18},
pages={1013-1036}
}

This paper presents algorithms for the assignment problem, the transportation problem, and the minimum-cost flow problem of operations research. The algorithms find a minimum-cost solution, yet run in time close to the best-known bounds for the corresponding problems without costs. For example, the assignment problem (equivalently, minimum-cost matching in a bipartite graph) can be solved in O(v/'rn log(nN)) time, where n, m, and N denote the number of vertices, number of edges, and largestâ€¦Â CONTINUE READING