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Accelerated Information Dissemination on Networks with Local and Global Edges

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Structural Information and Communication Complexity (SIROCCO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13298))

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Abstract

Bootstrap percolation is a classical model for the spread of information in a network. In the round-based version, nodes of an undirected graph become active once at least r neighbors were active in the previous round. We propose the perturbed percolation process: a superposition of two percolation processes on the same node set. One process acts on a local graph with activation threshold 1, the other acts on a global graph with threshold r – representing local and global edges, respectively. We consider grid-like local graphs and expanders as global graphs on n nodes.

For the extreme case \(r = 1\), all nodes are active after \(O(\log n)\) rounds, while the process spreads only polynomially fast for the other extreme case \(r \ge n\). For a range of suitable values of r, we prove that the process exhibits both phases of the above extremes: It starts with a polynomial growth and eventually transitions from at most cn to n active nodes, for some constant \(c \in (0, 1)\), in \(O(\log n)\) rounds. We observe this behavior also empirically, considering additional global-graph models.

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Acknowledgments

We thank David Peleg for suggesting this research direction and for multiple discussions, and Noga Alon for suggesting the proof of Theorem 8. This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 945298-ParisRegionFP.

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Authors and Affiliations

  1. School of Computer Science, The Academic College of Tel Aviv-Yaffo, Tel Aviv-Yaffo, Israel

    Sarel Cohen

  2. Hasso Plattner Institute, University of Potsdam, Potsdam, Germany

    Philipp Fischbeck & Tobias Friedrich

  3. Sorbonne University, CNRS, LIP6, Paris, France

    Martin S. Krejca

  4. Department of Computer Science and Technology, University of Cambridge, Cambridge, UK

    Thomas Sauerwald

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  1. Sarel Cohen
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  2. Philipp Fischbeck
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  4. Martin S. Krejca
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  5. Thomas Sauerwald
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Correspondence to Philipp Fischbeck .

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Editors and Affiliations

  1. Weizmann Institute, Rehovot, Israel

    Merav Parter

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Cohen, S., Fischbeck, P., Friedrich, T., Krejca, M.S., Sauerwald, T. (2022). Accelerated Information Dissemination on Networks with Local and Global Edges. In: Parter, M. (eds) Structural Information and Communication Complexity. SIROCCO 2022. Lecture Notes in Computer Science, vol 13298. Springer, Cham. https://doi.org/10.1007/978-3-031-09993-9_5

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  • DOI: https://doi.org/10.1007/978-3-031-09993-9_5

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