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A new approach to the maximum flow problem (1988)
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| Venue: | JOURNAL OF THE ACM |
| Citations: | 672 - 33 self |
BibTeX
@ARTICLE{Goldberg88anew,
author = {Andrew V. Goldberg and Robert E. Tarjan},
title = {A new approach to the maximum flow problem},
journal = {JOURNAL OF THE ACM},
year = {1988},
volume = {35},
number = {4},
pages = {921--940}
}
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Abstract
All previously known efficient maximum-flow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortest-length augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the preflow concept of Karzanov is introduced. A preflow is like a flow, except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out. The method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths. The algorithm and its analysis are simple and intuitive, yet the algorithm runs as fast as any other known method on dense. graphs, achieving an O(n³) time bound on an n-vertex graph. By incorporating the dynamic tree data structure of Sleator and Tarjan, we obtain a version of the algorithm running in O(nm log(n²/m)) time on an n-vertex, m-edge graph. This is as fast as any known method for any graph density and faster on graphs of moderate density. The algorithm also admits efticient distributed and parallel implementations. A parallel implementation running in O(n²log n) time using n processors and O(m) space is obtained. This time bound matches that of the Shiloach-Vishkin algorithm, which also uses n processors but requires O(n²) space.
Keyphrases
new approach maximum flow problem parallel implementation total amount alternative method fulkerson algorithm known method time bound match original network nm log layered network approach moderate density dynamic tree data structure shortest path efficient maximum-flow algorithm work shortest-length augmenting path preflow concept graph density n-vertex graph m-edge graph original ford shiloach-vishkin algorithm push local flow excess
