On the Average-Case Complexity of the Graph Reliability Problem on Gaussian Distributions

Authors:
Dmitri Burago;Michel de Rougemont
Affiliations:
(Correspd.) Department of Mathematics, Penn-State University, University Park, U.S.A. email address : burago@math.psu.edu;(Correspd.) Department of Computer Science, University Paris II, Paris, France. email address : mdr@lri.fr
Venue:
Fundamenta Informaticae
Year:
1998

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Abstract

We introduce classes of narrow graphs (including grid strips of fixed width), for which the graph reliability problem admits a polynomial time algorithm. Using this algorithm, we show that graph reliability is computable in polynomial time for the average complexity with respect to a Gaussian distribution. The latter is defined as follows: the vertices are numbered by integers {1,2, ...n}, and the probability that an edge between i and j is present is e −|i−j| 2.