Rumor spreading with bounded in-degree

Daum, Sebastian; Kühn, Fabian

doi:10.1016/j.tcs.2018.05.041

Cited by 5 publications

(2 citation statements)

References 11 publications

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“…Then by the union bound, we have P[T (n − u 0 , n) > r] ≤ P r := min{1, n −τ r+1−α }, that together with(11) proves the tail bound statement.Finally, E[T (n − u 0 , n)] ≤ 1 + r≥1 P r = O(1), for any u 0 ≤ n 1−α . Then, together with(10) it proves that E[T (n − gn , n)] ≤ log ln n + O(1).…”

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confidence: 75%

“…The first to discuss this issue are Daum, Kuhn, and Maus [10] (also the SIROCCO 2016 best paper). Among other results, they show that if only one incoming call can be answered and if this choice is taken adversarially, then there are networks where a previously polylogarithmic rumor spreading time of the pull protocol becomes Ω( √ n).…”

Section: Answering Single Calls Onlymentioning

confidence: 99%

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Randomized Rumor Spreading Revisited (Long Version)

Doerr¹

2023

Preprint

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We develop a simple and generic method to analyze randomized rumor spreading processes in fully connected networks. In contrast to all previous works, which heavily exploit the precise definition of the process under investigation, we only need to understand the probability and the covariance of the events that uninformed nodes become informed. This universality allows us to easily analyze the classic push, pull, and push-pull protocols both in their pure version and in several variations such as messages failing with constant probability or nodes calling a random number of others each round. Some dynamic models can be analyzed as well, e.g., when the network is a G(n, p) random graph sampled independently each round [Clementi et al. (ESA 2013)].Despite this generality, our method determines the expected rumor spreading time precisely apart from additive constants, which is more precise than almost all previous works. We also prove tail bounds showing that a deviation from the expectation by more than an additive number of r rounds occurs with probability at most exp(−Ω(r)).We further use our method to discuss the common assumption that nodes can answer any number of incoming calls. We observe that the restriction that only one call can be answered leads to a significant increase of the runtime of the push-pull protocol. In particular, the double logarithmic end phase of the process now takes logarithmic time. This also increases the message complexity from the asymptotically optimal Θ(n log log n) [Karp, Shenker, Schindelhauer, Vöcking (FOCS 2000)] to Θ(n log n). We propose a simple variation of the push-pull protocol that reverts back to the double logarithmic end phase and thus to the Θ(n log log n) message complexity.

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confidence: 75%

Section: Answering Single Calls Onlymentioning

confidence: 99%