Chip firing and all-terminal network reliability bounds

Jason I. Brown, Charles Colbourn, Richard J. Nowakowski

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The (all-terminal) reliability of a graph G is the probability that all vertices are in the same connected component, given that vertices are always operational but edges fail independently each with probability p. Computing reliability is #P-complete, and hence is expected to be intractable. Consequently techniques for efficiently (and effectively) bounding reliability have been the major thrust of research in the area. We utilize a deep connection between reliability and chip firings on graphs to improve previous bounds for reliability.

Original languageEnglish (US)
Pages (from-to)436-445
Number of pages10
JournalDiscrete Optimization
Issue number4
StatePublished - Nov 2009


  • All-terminal reliability
  • Bounds
  • Chip firing
  • Graph
  • M-partitionable
  • M-shelling
  • Multicomplex

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics


Dive into the research topics of 'Chip firing and all-terminal network reliability bounds'. Together they form a unique fingerprint.

Cite this