Finding Minimum-Cost Circulations by Successive Approximation,
Abstract
This document develops a new approach to solving minimum-cost circulation problems. This approach combines methods for solving the maximum flow problem with successive approximation techniques based on cost scaling. The authors measure the accuracy of a solution by the amount that the complementary slackness conditions are violated. They propose a simple minimum-cost circulation algorithm, one version of which runs in O(cu n log(nC)) time on an n-vertex network with integer arc costs of absolute value at most C. By incorporating sophisticated data structures into the algorithm, we obtain a time bound of O(nm log(sq n/m) log(nC)) on a network with m arcs. A slightly different use of our approach shows that a minimum-cost circulation can be computed by solving a sequence of O(n log(nC)) blocking slow problems. A corollary of this result is an O(sq n (log n) log (nC)-time, n-processor parallel minimum cost circulation algorithm. This approach also yields strongly polynomial minimum-cost circulation algorithms. Results provide evidence that the minimum-cost circulation problem is not much harder than the maximum flow problem. It is believed that a suitable implementation of this method will perform extremely well in practice. Keywords: Network flows.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1987
- Accession Number
- ADA194028
Entities
People
- Andrew V. Goldberg
- Robert Tarjan
Organizations
- Princeton University