Sparse reliable graph backbones

  title={Sparse reliable graph backbones},
  author={Shiri Chechik and Yuval Emek and Boaz Patt-Shamir and David Peleg},
  journal={Inf. Comput.},
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