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- W2091114846 abstract "In the probabilistic graph, SAT reliability may be defined as the probability that there exists at least one path consisting only of successful edges from s (source vertex) to every other vertex. The SDP method enumerates Boolean product terms corresponding to each of the minimal sets of edges (tree or cutset) whose success or failure results in successful or failed graph operation. The method then generates the reliability formula by transforming a Boolean sum of products into an equivalent form in which all terms are disjoint. However, this method has disadvantages in that in the process of transformation an intermediate product term should be compared with partially formed disjoint terms to determine the term to be retained or dropped, and the amount of computation time is dominated by the number of comparisons. This paper defines an optimal SAT reliability formula which is the one with a minimal number of product terms. Next, the expected property and ordering of the minimal sets for generating the optimal formula are discussed and some conditions are presented to obtain an optimal one whose number of terms is equal to the number of minimal sets. Furthermore, this paper proposes an optimal method which has a fundamental operation to enumerate spanning trees by edge reductions (open- or short-circuiting) and derives an optimal formula such that the number of terms in the SAT reliability formula is equal to the number of spanning trees and each term of the formula can be determined from a spanning tree and its particular chords without use of Boolean algebra. Since every term is determined directly without comparisons at a time when a tree is generated, it seems to result in less computation time and remarkable saving of the memory space compared with the SDP method using a set of minimal cutsets." @default.
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- W2091114846 date "1990-01-01" @default.
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- W2091114846 title "An optimal symbolic reliability expression using spanning trees for source-to-all-terminal systems" @default.
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- W2091114846 doi "https://doi.org/10.1002/ecjc.4430730205" @default.
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