Finding Minimum-Cost Flows by Double Scaling
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 U(nC)) time on networks with n vertices, m arcs, 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 of 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 (uncapacitated) transportation problem. In addition, we discuss a capacity-bounding approach to the minimum cost flow problem.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1988
- Accession Number
- ADA214498
Entities
People
- Andrew V. Goldberg
- James B. Orlin
- Ravindra K. Ahuja
- Robert Tarjan
Organizations
- Princeton University