Simplifying maximum flow computations: The effect of shrinking and good initial flows

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Details zur Publikation

Autorinnen und Autoren: Liers F, Pardella GL
Zeitschrift: Discrete Applied Mathematics
Verlag: Elsevier
Jahr der Veröffentlichung: 2011
Band: 159
Heftnummer: 17
Seitenbereich: 2187-2203
ISSN: 0166-218X


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 pushrelabel 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 (1990) [12] 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 computer vision, we show that a suitable combination of the proposed techniques speeds up traditionally used methods. © 2011 Elsevier B.V. All rights reserved.

FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Liers-Bergmann, Frauke Prof. Dr.
Professur für Angewandte Mathematik (Ganzzahlige und robuste Optimierung)

Einrichtungen weiterer Autorinnen und Autoren

Universität Köln


Liers, F., & Pardella, G.L. (2011). Simplifying maximum flow computations: The effect of shrinking and good initial flows. Discrete Applied Mathematics, 159(17), 2187-2203.

Liers, Frauke, and Gregor L. Pardella. "Simplifying maximum flow computations: The effect of shrinking and good initial flows." Discrete Applied Mathematics 159.17 (2011): 2187-2203.


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