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( K, j )‐domination and ( K, j )‐reliability
Author(s) -
Rodriguez Jose,
Traldi Lorenzo
Publication year - 1997
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/(sici)1097-0037(199712)30:4<293::aid-net6>3.0.co;2-e
Subject(s) - reliability (semiconductor) , subnetwork , terminal (telecommunication) , factoring , computation , reliability theory , mathematics , combinatorics , computer science , discrete mathematics , algorithm , power (physics) , statistics , physics , computer network , failure rate , finance , quantum mechanics , economics
The ( K, j )‐reliability of a K ‐terminal network G is the probability that after the failure of some of its edges the vertices in K will lie in no more than j connected components of the resulting subnetwork of G ; when j = 1, this is the usual K ‐terminal reliability of G . In this paper, we extend the well‐known theory of reliability domination and its application to the analysis of factoring algorithms for the computation of K ‐terminal reliability to ( K, j )‐reliability and the associated notion of ( K, j )‐domination. We give conditions equivalent to two edges being parallel or in series with respect to ( K, j )‐reliability, and we characterize the networks of ( K, j )‐domination ≥ 3. © 1997 John Wiley & Sons, Inc. Networks 30: 293–306, 1997