Abstract
In the gossip-based model of communication for disseminating information in a network, in each time unit, every node u can contact a single random neighbor v but can possibly be contacted by many nodes. In the present paper, we consider a restricted model where at each node only one incoming call can be answered in one time unit. We study the implied weaker version of the well-studied pull protocol, which we call restricted pull.
We prove an exponential separation of the rumor spreading time between two variants of the protocol (the answered call among a set of calls is chosen adversarial or uniformly at random). Further, we show that if the answered call is chosen randomly, the slowdown of restricted pull versus the classic pull protocol can w.h.p. be upper bounded by \(O(\varDelta / \delta \cdot \log n)\), where \(\varDelta \) and \(\delta \) are the largest and smallest degree of the network.
A full version of this paper with all proofs is avalaible on https://arxiv.org/abs/1506.00828 [1].
Second and third author supported by ERC Grant No. 336495 (ACDC).
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Notes
- 1.
Here \(\tilde{O}\) hides \(\log (n)\) factors.
- 2.
Actually, \(\frac{\varDelta }{\delta }\) can be replaced by \(\max _{\left\{ u,v\right\} \in E} d_{}(u)/d_{}(v)\) in all parts of the paper, where \(d_{}(u)\) and \(d_{}(v)\) denote the degrees of the nodes.
- 3.
A set \(F\subseteq \mathcal {S}\) is called monotone if \(A\in F\) and \(A\preceq _{\mathcal {S}}B\) implies \(B\in F\).
- 4.
Figure 2 can be used to verify this.
References
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Daum, S., Kuhn, F., Maus, Y. (2016). Rumor Spreading with Bounded In-Degree. In: Suomela, J. (eds) Structural Information and Communication Complexity. SIROCCO 2016. Lecture Notes in Computer Science(), vol 9988. Springer, Cham. https://doi.org/10.1007/978-3-319-48314-6_21
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