A linear time 2 + ε approximation algorithm for edge connectivity
David W. Matula
- pp 500-504
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This article is published in Symposium on Discrete Algorithms.The article was published on 1993-01-01 and is currently open access. It has received 71 citations till now. The article focuses on the topics: Best bin first & Nearest neighbor graph.read more
Citations
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A simple min-cut algorithm
Mechthild Stoer,Frank Wagner +1 more
TL;DR: An algorithm for finding the minimum cut of an undirected edge-weighted graph that has a short and compact description, is easy to implement, and has a surprisingly simple proof of correctness.
Journal ArticleDOI
A new approach to the minimum cut problem
David R. Karger,Clifford Stein +1 more
TL;DR: A randomized, strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability with a significant improvement over the previous time bounds based on maximum flows.
Proceedings ArticleDOI
A matroid approach to finding edge connectivity and packing arborescences
TL;DR: An algorithm that finds k edge-disjoint arborescences on a directed graph in time O(kmn + k3n2)2 is presented, based on two theorems of Edmonds that link these two problems and show how they can be solved.
Journal ArticleDOI
Random Sampling in Cut, Flow, and Network Design Problems
TL;DR: It is shown that the sparse graph, or skeleton, that arises when the authors randomly sample a graph's edges will accurately approximate the value of all cuts in the original graph with high probability, which makes sampling effective for problems involving cuts in graphs.
Proceedings ArticleDOI
Random sampling in cut, flow, and network design problems
TL;DR: It is shown that the sparse graph, or skeleton, that arises when the authors randomly sample a graph's edges will accurately approximate the value of all cuts in the original graph with high probability, which makes sampling effective for problems involving cuts in graphs.
References
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Network Flow and Testing Graph Connectivity
Shimon Even,R. Endre Tarjan +1 more
TL;DR: An algorithm of Dinic for finding the maximum flow in a network is described and it is shown that if the vertex capacities are all equal to one, the algorithm requires at most $O(|V|^{1/2} \cdot |E|)$ time.
Proceedings ArticleDOI
Determining edge connectivity in 0(nm)
TL;DR: An algorithm that determines the edge connectivity of an n-vertex m-edge graph G in O(nm) time is described and a refinement shows that the question as to whether a graph is k-edge connected can be determined in O (kn2), for dense graphs characterized by m = Ω(n2).
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On computing the connectivities of graphs and digraphs
TL;DR: Methods are described that will compute the edge-connectivity of a graph or a digraph at least twice as fast as the known methods, and compare favorably with Kleitman's, Even, Even and Tarjan's, and Galil's algorithms.
Proceedings ArticleDOI
Efficient parallel algorithms for testing connectivity and finding disjoint s-t paths in graphs
Samir Khuller,Baruch Schieber +1 more
TL;DR: An efficient parallel algorithm for testing whether a graph G is K-vertex connected, for any fixed k, is presented and it is shown how to modify the algorithm to find k-edge disjoint paths, if they exist.
Journal ArticleDOI
Extracting maximal information about sets of minimum cuts
Dan Gusfield,Dalit Naor +1 more
TL;DR: This paper shows how to marry two well-known, elegant, compact, and efficiently computed representations of selected minimum edge cuts in a weighted, undirected graphG, and demonstrates how to find all pairs of nodes that are separated by at least one connectivity cut inO(nm) time.