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• W3217740702 abstract "Consider a graph with perfect nodes and edges subject to independent random failures with identical probability. The <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>all-terminal reliability</i> is the probability that the resulting subgraph is connected. First, we fully characterize uniformly least reliable graphs (ULRG) whose co-rank is not greater than four. Universal reliability bounds are here introduced for those graphs. It is formally proved that ULRG is invariant under bridge-contractions, and maximize the number of bridges among all connected simple graphs with a prescribed number of nodes and edges. A closed-form for the maximum number of bridges is also given, which has an intrinsic interest from a graph-theoretic point of view. Finally, the cost-reliability tradeoff is discussed, comparing the number of edges required to reduce the reliability gaps between the least and most reliable graphs. A remarkable conclusion is that the network design is critical under rare event failures, where the reliability-gap between least and most-reliable networks is monotonically increasing with the number of terminals." @default.
• W3217740702 created "2021-12-06" @default.
• W3217740702 creator A5007780223 @default.
• W3217740702 date "2022-03-01" @default.
• W3217740702 modified "2023-09-25" @default.
• W3217740702 title "Universal Reliability Bounds for Sparse Networks" @default.
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• W3217740702 doi "https://doi.org/10.1109/tr.2021.3061075" @default.
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