Generalized Random Sequential Adsorption on Erdős–Rényi Random Graphs

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

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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

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Random Sequential Adsorption
Random Graphs
apexes
adsorption
Vertex of a graph
Jamming
Graph in graph theory
Greedy Algorithm
Independent Set
greedy algorithms
Nearest Neighbor
Proportion
Limiting
jamming
Generalise
proportion

Keywords

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

Cite this

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Generalized Random Sequential Adsorption on Erdős–Rényi Random Graphs. / Dhara, S.; van Leeuwaarden, J.S.H.; Mukherjee, D.

In: Journal of Statistical Physics, Vol. 164, No. 5, 01.09.2016, p. 1217-1232.

Research output: Contribution to journalArticleAcademicpeer-review

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