Accelerated Information Dissemination on Networks with Local and Global Edges

Sarel Cohen, Philipp Fischbeck*, Tobias Friedrich, Martin S. Krejca, Thomas Sauerwald

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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≥ 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∈ (0, 1 ), in O(log n) rounds. We observe this behavior also empirically, considering additional global-graph models.

Original languageEnglish
Title of host publicationStructural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Proceedings
EditorsMerav Parter
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages19
ISBN (Print)9783031099922
StatePublished - 2022
Externally publishedYes
Event29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022 - Paderborn, Germany
Duration: 27 Jun 202229 Jun 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13298 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference29th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2022


  • Bootstrap percolation
  • Expanders
  • Random graphs
  • Rumor spreading


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