偏置表示在边连通性和图刚性中的应用

H. Gabow
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引用次数: 101

摘要

研究了由标记算法定义的一组集合的偏序集表示。给出了图的最小割族的偏序集表示,并给出了如何快速计算它们的方法。这些表示是增加图边缘连通性的算法的起点,从lambda到给定目标tau = lambda + delta,添加尽可能少的边。对于无向图,时间边界本质上是检验tau边连通性的最著名的边界;对于有向图,时间范围大致是一个因子。当图对由刚性条构成的结构进行建模时,还构造了图的刚性子图族的偏置表示。这些问题之间的联系是它们都处理图形拟阵。
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Applications of a poset representation to edge connectivity and graph rigidity
A poset representation for a family of sets defined by a labeling algorithm is investigated. Poset representations are given for the family of minimum cuts of a graph, and it is shown how to compute them quickly. The representations are the starting point for algorithms that increase the edge connectivity of a graph, from lambda to a given target tau = lambda + delta , adding the fewest edges possible. For undirected graphs the time bound is essentially the best-known bound to test tau -edge connectivity; for directed graphs the time bound is roughly a factor delta more. Also constructed are poset representations for the family of rigid subgraphs of a graph, when graphs model structures constructed from rigid bars. The link between these problems is that they all deal with graphic matroids.<>
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