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Rapid Almost-Complete Broadcasting in Faulty Networks

Rastislav Královič·Richard Královič
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Abstract

This paper studies the problem of broadcasting in synchronous point-to-point networks, where one initiator owns a piece of information that has to be transmitted to all other vertices as fast as possible. The model of fractional dynamic faults with threshold is considered: in every step either a fixed number $T$, or a fraction $α$, of sent messages can be lost depending on which quantity is larger. As the main result we show that in complete graphs and hypercubes it is possible to inform all but a constant number of vertices, exhibiting only a logarithmic slowdown, i.e. in time $O(D\log n)$ where $D$ is the diameter of the network and $n$ is the number of vertices. Moreover, for complete graphs under some additional conditions (sense of direction, or $α<0.55$) the remaining constant number of vertices can be informed in the same time, i.e. $O(\log n)$.

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Rastislav Královič, Richard Královič. 2007-03-23. Rapid Almost-Complete Broadcasting in Faulty Networks. https://arxiv.org/abs/cs/0703122

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