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Communication Dans Un Congrès Année : 2022

Accelerated Information Dissemination on Networks with Local and Global Edges

Résumé

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 rrepresenting 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.
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Dates et versions

hal-03646955 , version 1 (20-04-2022)

Identifiants

Citer

Sarel Cohen, Philipp Fischbeck, Tobias Friedrich, Martin Krejca, Thomas Sauerwald. Accelerated Information Dissemination on Networks with Local and Global Edges. 29th International Colloquium on Structural Information and Communication Complexity (SIROCCO), Jun 2022, Paderborn, Germany. pp.79-97, ⟨10.1007/978-3-031-09993-9_5⟩. ⟨hal-03646955⟩
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