Institution: Stanford University, Department of Computer Science

Title: Finding Minimum-Cost Flows by Double-Scaling

Author: Ahuja, R. K.

Author: Goldberg, A. V.

Author: Orlin, J. B.

Author: Tarjan, R. E.

Date: October 1988

Abstract: Several researchers have recently developed new techniques that give fast algorithms for the minimum-cost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm log log Ulog(nC)) time on networks with n vertices, m edges, maximum arc capacity U, and maximum arc cost magnitude C. The major techniques used are the capacity-scaling approach of Edmonds and Karp, the excess-scaling approach of Ahuja and Orlin, the cost-scaling approach Goldberg and Tarjan, and the dynamic tree data structure of Sleator and Tarjan. For nonsparse graphs with large maximum arc capacity, we obtain a similar but slightly better bound. We also obtain a slightly better bound for the (noncapacitated) transportation problem. In addition, we discuss a capacity-bounding approach to the minimum-cost flow problem.

http://i.stanford.edu/pub/cstr/reports/cs/tr/88/1227/CS-TR-88-1227.pdf