Chip firing and all-terminal network reliability bounds

Authors:
Jason I. Brown;Charles J. Colbourn;Richard J. Nowakowski
Affiliations:
Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada B3H 3J5;Computer Science and Engineering, Arizona State University, PO Box 878809, Tempe, AZ 85287-8809, USA;Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada B3H 3J5
Venue:
Discrete Optimization
Year:
2009

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Abstract

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.