Computing Vertex Connectivity: New Bounds from Old Techniques
نویسندگان
چکیده
منابع مشابه
Computing Vertex Connectivity: New Bounds from Old Techniques
The vertex connectivity k of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known deterministic algorithm for finding the vertex connectivity and a corresponding Ž 3 separator. The time for a digraph having n vertices and m edges is O min k q 4 . n, k n m ; for an undirected graph the term m can be replaced by k n. A ran...
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Given a capacitated graph G = (V, E) and a set of terminals K ⊆ V , how should we produce a graph H only on the terminals K so that every (multicommodity) flow between the terminals in G could be supported in H with low congestion, and vice versa? (Such a graph H is called a flow-sparsifier for G.) What if we want H to be a “simple” graph? What if we allow H to be a convex combination of simple...
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Given a capacitated graph G = (V,E) and a set of terminals K ⊆ V , how should we produce a graph H only on the terminals K so that every (multicommodity) flow between the terminals in G could be supported in H with low congestion, and vice versa? (Such a graph H is called a flowsparsifier for G.) What if we want H to be a “simple” graph? What if we allow H to be a convex combination of simple g...
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A fundamental result by Karger [10] states that for any λ-edgeconnected graph with n nodes, independently sampling each edge with probability p = Ω(logn/λ) results in a graph that has edge connectivity Ω(λp), with high probability. This paper proves the analogous result for vertex connectivity, when sampling vertices. We show that for any k-vertex-connected graph G with n nodes, if each node is...
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ژورنال
عنوان ژورنال: Journal of Algorithms
سال: 2000
ISSN: 0196-6774
DOI: 10.1006/jagm.1999.1055