Consecutive cuts and paths, and bounds on k‐terminal reliability

Heidi J. Strayer, Charles J. Colbourn

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4 Scopus citations


Shanthikumar developed an upper bound for two‐terminal reliability based on consecutive s – t cutsets. Subsequently, Shier generalized this strategy to obtain upper bounds from cutsets, and lower bounds from pathsets, when the cutsets or pathsets form a semilattice structure. We examine a restricted case of Shier's method that yields a k‐terminal lower bound based on consecutive pathsets. Our approach employs a common reduction of consecutive cut and path bounds to the computation of the two‐terminal reliability of an interval graph with imperfect vertices. Computational results are given to support the observation that the consecutive paths lower bound is competitive with the best efficiently computable bounds that are currently available. We then apply the consecutive path bound to reduce, in some cases dramatically, the number of states generated in a most probable state bounding method.

Original languageEnglish (US)
Pages (from-to)165-175
Number of pages11
Issue number3
StatePublished - May 1995
Externally publishedYes

ASJC Scopus subject areas

  • Information Systems
  • Computer Networks and Communications

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