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SODA
1992
ACM

Computing Minimal Spanning Subgraphs in Linear Time

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Computing Minimal Spanning Subgraphs in Linear Time
Let P be a property of undirected graphs. We consider the following problem: given a graph G that has property P, nd a minimal spanning subgraph of G with property P. We describe general algorithms for this problem and prove their correctness under fairly weak assumptions about P. We establish that the worst-case running time of these algorithms is m+nlog n for 2-edge-connectivity and biconnectivity where n and m denote the number of vertices and edges, respectively, in the input graph. By re ning the basic algorithms we obtain the rst linear time algorithms for computing a minimal 2-edge-connected spanning subgraph and for computing a minimal biconnected spanning subgraph. We also devise general algorithms for computing a minimal spanning subgraph in directed graphs. These algorithms allow us to simplify an earlier algorithm of Gibbons, Karp, Ramachandran, Soroker and Tarjan for computing a minimal strongly connected spanning subgraph. We also provide the rst tight analysis of the la...
Xiaofeng Han, Pierre Kelsen, Vijaya Ramachandran,
Added 07 Nov 2010
Updated 07 Nov 2010
Type Conference
Year 1992
Where SODA
Authors Xiaofeng Han, Pierre Kelsen, Vijaya Ramachandran, Robert Endre Tarjan
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