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Reliability Polynomials of Networks with Vertex Failure
2009 International Conference on Computational Intelligence and Security, 2009For a graph $G$ with perfectly reliable edges and unreliable vertices, we consider the reliability of $G$ for which vertices fail independently of each other with a constant probability $p$. The reliability of graph $G$, denoted by $P_n(G, p)$, is defined to be the probability that the induced subgraphs of surviving vertices connected.
Haixing Zhao, Liang Wei
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Reliable determination of interpolating polynomials
Numerical Algorithms, 1993This paper solves an interpolation problem that is to determine a polynomial interpolant to specified data. The data can be taken as a set of points, at each of which a function value and any number of leading derivative values of the function are specified. An algorithm is described that delivers the required polynomial in Chebyshev form.
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Polynomial hash functions are reliable
1992Polynomial hash functions are well studied and widely used in various applications. They have gained popularity because of certain performances they exhibit. It has been shown that even linear hash functions are expected to have such performances. However, quite often we would like the hash functions to be reliable, meaning that they perform well with ...
Martin Dietzfelbinger +3 more
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Inflection points of reliability polynomials are dense in [0,1]
Networks, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jason I. Brown, Danielle Cox
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Computational Complexity of Coherent Systems and the Reliability Polynomial
Probability in the Engineering and Informational Sciences, 1988There are three general methods for system reliability evaluation, namely; (1) inclusion–exclusion, (2) sum of disjoint products, and (3) pivoting. Of these, only pivoting can be applied directly to a logic tree or network graph representation without first finding minimal path (or cut) sets.
Barlow, R. E., Iyer, S.
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Bounds on the Reliability Polynomial for Shellable Independence Systems
SIAM Journal on Algebraic Discrete Methods, 1982The reliability polynomial associated with an independence system is $g ( p ) = \sum_{k = 0}^n f_k p^k ( 1 - p )^{n - k} $, where $f_k $ is the number of independent sets of cardinality k and n is the cardinality of the ground set. An independence system $( T,\Gamma )$ is shellable if all maximal independent sets have the same cardinality and if there ...
Ball, Michael O., Provan, J. Scott
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Network utility problem and easy reliability polynomials
2016 8th International Workshop on Resilient Networks Design and Modeling (RNDM), 2016We model a communication system by a network, were the terminals are perfect but links may fail randomly, with identical probability q = 1 - p. This defines a partial random network. The all-terminal reliability R(p) is the probability that this random graph is connected, and it is a polynomial in p. Finding the reliability polynomial can be reduced to
Eduardo A. Canale +3 more
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Topologically Reliable Approximation of Trimmed Polynomial Surface Patches
Graphical Models and Image Processing, 1999Summary: The authors present an unstructured triangular mesh generation algorithm that approximates a set of mutually nonintersecting simple trimmed polynomial parametric surface patches within a user specified geometric tolerance. The proposed method uses numerically robust interval geometric representations/computations and also addresses the problem
Wonjoon Cho +3 more
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Reliability Hosoya-Wiener Polynomial of Double Weighted Trees
Fundamenta Informaticae, 2016Reliability Hosoya-Wiener polynomial for edge weighted graphs is defined, that can be used as a measure of reliability of a communication network. Each edge is assigned two weights, reliability and communication delay. Some basic properties are given and a recursive formula for the reliability Hosoya-Wiener polynomial of a rooted ...
Darja Rupnik Poklukar, Janez Zerovnik
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Computing Network Reliability in Time Polynomial in the Number of Cuts
Operations Research, 1984We present a new algorithm that computes the probability that there is an operating path from a node s to a node t in a stochastic network. The computation time of this algorithm is bounded by a polynomial in the number of (s, t)-cuts in the network. We also examine the complexity of other connectedness reliability problems with respect to the number ...
J. Scott Provan, Michael O. Ball
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