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# Sparse reliable graph backbones

@article{Chechik2012SparseRG, title={Sparse reliable graph backbones}, author={Shiri Chechik and Yuval Emek and Boaz Patt-Shamir and David Peleg}, journal={Inf. Comput.}, year={2012}, volume={210}, pages={31-39} }

- Published 2012 in Inf. Comput.
DOI:10.1016/j.ic.2011.10.007

Given a connected graph G and a failure probability pe for each edge e in G, the reliability of G is the probability that G remains connected when each edge e is removed independently with probability pe. In this paper it is shown that every n-vertex graph contains a sparse backbone, i.e., a spanning subgraph with O(n log n) edges whose reliability is at least (1−n−Ω(1)) times that ofG. Moreover, for any pair of vertices s, t in G, the (s, t)-reliability of the backbone, namely, the probability… CONTINUE READING