The smallest networks on which the Ford-Fulkerson maximum flow procedure may fail to terminate
Theoretical Computer Science
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Partial Augment---Relabel Algorithm for the Maximum Flow Problem
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Contraction network for solving maximum flow problem
Proceedings of the ACM SIGKDD Workshop on Mining Data Semantics
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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 (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.