Abstract
A classical algorithm for finding a minimum-cost circulation consists of repeatedly finding a residual cycle of negative cost and canceling it by pushing enough flow around the cycle to saturate an arc. We show that a judicious choice of cycles for canceling leads to a polynomial bound on the number of iterations in this algorithm. This gives a very simple strongly polynomial algorithm that uses no scaling. A variant of the algorithm that uses dynamic trees runs in Ο1989min{log(nC), m log n}) time on a network of n vertices, m arcs, and arc costs of maximum absolute value C. This bound is comparable to those of the fastest previously known algorithms.
Original language | English (US) |
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Pages (from-to) | 873-886 |
Number of pages | 14 |
Journal | Journal of the ACM (JACM) |
Volume | 36 |
Issue number | 4 |
DOIs | |
State | Published - Jan 10 1989 |
All Science Journal Classification (ASJC) codes
- Software
- Control and Systems Engineering
- Information Systems
- Hardware and Architecture
- Artificial Intelligence