The study of graphs reliability polynomials is of both theoretical and practical interest. Generally, the problem of reliability polynomial calculation is NP-hard. In this paper we find analytic solution of this probl...
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The study of graphs reliability polynomials is of both theoretical and practical interest. Generally, the problem of reliability polynomial calculation is NP-hard. In this paper we find analytic solution of this probl...
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ISBN:
(纸本)9781665464819
The study of graphs reliability polynomials is of both theoretical and practical interest. Generally, the problem of reliability polynomial calculation is NP-hard. In this paper we find analytic solution of this problem in some practical cases. Thus, linear complexity algorithm is offered for calculation of reliability of rectangular lattice strip. Graphs of this type can be used to model the topology of wireless sensor networks used to monitor long engineering infrastructure objects, such as pipeline systems. Sensors can be installed on the pipeline, inside it, or placed in the environment near the controlled object. To increase the efficiency of detecting events of interest, pairs of sensors operating on different physical principles can be used. By connecting paired sensors and neighboring homogeneous sensors with channels, we obtain a topology that is a rectangular lattice strip. However, this topology has advantages over linear sensor networks only if the channel reliability is high enough. Corresponding investigations have been presented in the paper.
In this paper some new ideas are presented concerning speeding up calculation of coefficients of all-terminal reliability polynomial (CRPs) of an undirected random graph with reliable nodes and unreliable links. Along...
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ISBN:
(数字)9781728154534
ISBN:
(纸本)9781728154541
In this paper some new ideas are presented concerning speeding up calculation of coefficients of all-terminal reliability polynomial (CRPs) of an undirected random graph with reliable nodes and unreliable links. Along with the task of obtaining exact values of CRPs , the task of their fast estimation is discussed. We try estimate CRPs in one of possible representations of reliability polynomial (RP) based on their meaning and counting all a fortiori connected and disconnected states of a graph using easily obtained information. We show how several steps of known exact methods anticipatory to calculation of CRPs bounds increase their quality.
In this book, we provide a comprehensive introduction to the most recentadvances in the application of machine learning methods in quantum sciences. Wecover the use of deep learning and kernel methods in supervised, u...
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