Sparse reliable graph backbones

Shiri Chechik, Yuval Emek, Boaz Patt-Shamir*, David Peleg

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Given a connected graph G and a failure probability p(e) 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 p(e). In this paper it is shown that every n-vertex graph contains a sparse backbone, i.e., a spanning subgraph with O(nlogn) edges whose reliability is at least (1-n- Ω(1)) times that of G. Moreover, for any pair of vertices s, t in G, the (s,t)-reliability of the backbone, namely, the probability that s and t remain connected, is also at least (1-n- Ω(1)) times that of G. Our proof is based on a polynomial time randomized algorithm for constructing the backbone. In addition, it is shown that the constructed backbone has nearly the same Tutte polynomial as the original graph (in the quarter-plane x≥1, y>1), and hence the graph and its backbone share many additional features encoded by the Tutte polynomial.

Original languageEnglish
Pages (from-to)31-39
Number of pages9
JournalInformation and Computation
StatePublished - Jan 2012


FundersFunder number
Israel Science Foundation1372/09
Ministry of Science and Technology, Israel


    • Network reliability
    • Sparse subgraphs
    • Tutte polynomial


    Dive into the research topics of 'Sparse reliable graph backbones'. Together they form a unique fingerprint.

    Cite this