Generalized Random Sequential Adsorption on Erdős–Rényi Random Graphs

S. Dhara, J.S.H. van Leeuwaarden, D. Mukherjee

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    91 Citations (Scopus)
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    Abstract

    We investigate random sequential adsorption (RSA) on a random graph via the following greedy algorithm: Order the n vertices at random, and sequentially declare each vertex either active or frozen, depending on some local rule in terms of the state of the neighboring vertices. The classical RSA rule declares a vertex active if none of its neighbors is, in which case the set of active nodes forms an independent set of the graph. We generalize this nearest-neighbor blocking rule in three ways and apply it to the Erdős–Rényi random graph. We consider these generalizations in the large-graph limit n→ ∞ and characterize the jamming constant, the limiting proportion of active vertices in the maximal greedy set.

    Original languageEnglish
    Pages (from-to)1217-1232
    Number of pages16
    JournalJournal of Statistical Physics
    Volume164
    Issue number5
    Early online date20 Jul 2016
    DOIs
    Publication statusPublished - 1 Sep 2016

    Keywords

    • Frequency assignment
    • Greedy independent set
    • Jamming limit
    • Parking problem
    • Random graphs
    • Random sequential adsorption

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