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Towards Constant Time Multi-Call Rumor Spreading on Small-Set Expanders

Authors Emilio Cruciani , Sebastian Forster , Tijn de Vos

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ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Probabilistic algorithms
Keywords
  • small set expansion
  • vertex expansion
  • rumor spreading
  • multi-call rumor spreading
  • push&pull protocol

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Abstract

We study a multi-call variant of the classic PUSH&PULL rumor spreading process where nodes can contact k of their neighbors instead of a single one during both PUSH and PULL operations. We show that rumor spreading can be made faster at the cost of an increased amount of communication between the nodes. As a motivating example, consider the process on a complete graph of n nodes: while the standard PUSH&PULL protocol takes Θ(log n) rounds, we prove that our k-PUSH&PULL variant completes in Θ(log_{k} n) rounds, with high probability.
We generalize this result in an expansion-sensitive way, as has been done for the classic PUSH&PULL protocol for different notions of expansion, e.g., conductance and vertex expansion. We consider small-set vertex expanders, graphs in which every sufficiently small subset of nodes has a large neighborhood, ensuring strong local connectivity. In particular, when the expansion parameter satisfies ϕ > 1, these graphs have a diameter of o(log n), as opposed to other standard notions of expansion. Since the graph’s diameter is a lower bound on the number of rounds required for rumor spreading, this makes small-set expanders particularly well-suited for fast information dissemination. We prove that k-PUSH&PULL takes O(log_{ϕ} n ⋅ log_{k} n) rounds in these expanders, with high probability. We complement this with a simple lower bound of Ω(log_{ϕ} n+ log_{k} n) rounds.

Cite As Get BibTex

Emilio Cruciani, Sebastian Forster, and Tijn de Vos. Towards Constant Time Multi-Call Rumor Spreading on Small-Set Expanders. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 26:1-26:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DISC.2025.26

Author Details

Emilio Cruciani
  • European University of Rome, Italy
Sebastian Forster
  • University of Salzburg, Austria
Tijn de Vos
  • TU Graz, Austria

Funding

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 947702) and is supported by the Austrian Science Fund (FWF): P 32863-N and P 36280-N.

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