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arXiv 1201.0435cs.ITcs.NImath.IT
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点对点网络的容量因子

Capacity Factors of a Point-to-point Network

Yuan Li, Yue Zhao, Haibin Kan

摘要:

本文研究了网络编码链路失效问题中容量因子的一些性质。网络的容量因子(CF)是一个边集,删除边集会导致最大流减少,而删除任意一个真子集则不会。通常,$k$ -CF是将导致网络最大流减少$k$的最小(非最小)边缘集。在点到点的非循环场景下,我们刻画了包含在CF中的所有边,并提出了一种有效的分类算法。证明了非循环点到点非循环网络中某些$s$ - $t$路上的所有边都包含在某些2-CF中。本文还研究了点到点网络中CF的其他性质,以及在多播网络中CF与CF的简单关系。另一方面,得到了一些与容量因子有关的计算困难结果。证明了判定一个循环网络是否存在容量因子是NP-完全的,并且通过求解最大流使计算容量秩的时间复杂度有界降低.此外,我们提出了类似的定义CF的顶点,并表明它捕获的边缘容量因子作为一种特殊情况。

英文摘要:

In this paper, we investigate some properties on capacity factors, which were proposed to investigate the link failure problem from network coding. A capacity factor (CF) of a network is an edge set, deleting which will cause the maximum flow to decrease while deleting any proper subset will not. Generally, a $k$-CF is a minimal (not minimum) edge set which will cause the network maximum flow decrease by $k$. Under point to point acyclic scenario, we characterize all the edges which are contained in some CF, and propose an efficient algorithm to classify. And we show that all edges on some $s$-$t$ path in an acyclic point-to-point acyclic network are contained in some 2-CF. We also study some other properties of CF of point to point network, and a simple relationship with CF in multicast network. On the other hand, some computational hardness results relating to capacity factors are obtained. We prove that deciding whether there is a capacity factor of a cyclic network with size not less a given number is NP-complete, and the time complexity of calculating the capacity rank is lowered bounded by solving the maximal flow. Besides that, we propose the analogous definition of CF on vertices and show it captures edge capacity factors as a special case.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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