网络中的瓶颈流

摘要：

瓶颈网络流问题（BNFP）是瓶颈运输问题（BTP）、瓶颈分配问题（BAP）、瓶颈路径问题（BPP）等瓶颈问题的推广，本文综述了这一问题的重要结果及其各种特殊情况。我们观察到，BNFP可以解决作为一个序列的$O(\log n)$最大流问题。然而，可以修改用于最大流问题的基于特殊增广路径的算法以获得用于BNFP的算法，该算法具有这些变化和相应的最大流算法具有相同的最坏情况时间复杂度的性质。在单位容量网络上，我们证明了BNFP可以在$O(\min \{{m(n\log n)}^{2/3}, m^{3/2}\sqrt{\log n}\})$中求解。这将最佳可用算法改进了$\sqrt{\log n}$的因子。在单位容量简单图上，证明了BNFP问题可以在$O(m \sqrt {n \log n})$时间内求解.因此，我们有一个$O(m \sqrt {n \log n})$算法的BTP与单位弧容量。

英文摘要：

The bottleneck network flow problem (BNFP) is a generalization of several well-studied bottleneck problems such as the bottleneck transportation problem (BTP), bottleneck assignment problem (BAP), bottleneck path problem (BPP), and so on. In this paper we provide a review of important results on this topic and its various special cases. We observe that the BNFP can be solved as a sequence of $O(\log n)$ maximum flow problems. However, special augmenting path based algorithms for the maximum flow problem can be modified to obtain algorithms for the BNFP with the property that these variations and the corresponding maximum flow algorithms have identical worst case time complexity. On unit capacity network we show that BNFP can be solved in $O(\min \{{m(n\log n)}^{2/3}, m^{3/2}\sqrt{\log n}\})$. This improves the best available algorithm by a factor of $\sqrt{\log n}$. On unit capacity simple graphs, we show that BNFP can be solved in $O(m \sqrt {n \log n})$ time. As a consequence we have an $O(m \sqrt {n \log n})$ algorithm for the BTP with unit arc capacities.

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