Simplifying Maximum Flow Computations: the Effect of Shrinking and Good Initial Flows
Liers, Frauke and Pardella, Gregor
(2011)
Simplifying Maximum Flow Computations: the Effect of Shrinking and Good Initial Flows.
Published in:
Discrete Applied Mathematics Vol. 159 (17).
2187 -2203.
Abstract
Maximum-flow problems occur in a wide range of applications. Although already well-studied, they are still an area of active research. The fastest available implementations for determining maximum flows in graphs are either based on augmenting-path or on push-relabel algorithms. In this work, we present two ingredients that, appropriately used, can considerably speed up these methods. On the theoretical side, we present flow-conserving conditions under which subgraphs can be contracted to a single vertex. These rules are in the same spirit as presented by Padberg and Rinaldi (Math. Programming (47), 1990) for the minimum cut problem in graphs. These rules allow the reduction of known worst-case instances for different maximum flow algorithms to equivalent trivial instances. On the practical side, we propose a two-step max-flow algorithm for solving the problem on instances coming from physics and computer vision. In the two-step algorithm flow is first sent along augmenting paths of restricted lengths only. Starting from this flow, the problem is then solved to optimality using some known max-flow methods. By extensive experiments on instances coming from applications in theoretical physics and in computer vision, we show that a suitable combination of the proposed techniques speeds up traditionally used methods.
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Editorial actions: | ![]() |
Item Type: | Article |
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Citations: | 0 (Google Scholar) | 0 (Web of Science) |
Uncontrolled Keywords: | maximum flow minimum cut subgraph shrinking hybrid algorithm |
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Divisions: | Institute of Computer Science > Projects > COPhy (Combinatorial Optimization in Physics) |
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ZAIK Number: | zaik2011-625 |
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Depositing User: | Frauke Liers |
Date Deposited: | 27 Jun 2011 00:00 |
Last Modified: | 09 Jan 2012 11:27 |
URI: | http://e-archive.informatik.uni-koeln.de/id/eprint/625 |