### 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 language | English |
---|---|

Pages (from-to) | 1217-1232 |

Number of pages | 16 |

Journal | Journal of Statistical Physics |

Volume | 164 |

Issue number | 5 |

Early online date | 20 Jul 2016 |

DOIs | |

Publication status | Published - 1 Sep 2016 |

### Fingerprint

### Keywords

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

### Cite this

*Journal of Statistical Physics*,

*164*(5), 1217-1232. https://doi.org/10.1007/s10955-016-1583-z

}

*Journal of Statistical Physics*, vol. 164, no. 5, pp. 1217-1232. https://doi.org/10.1007/s10955-016-1583-z

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

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Generalized Random Sequential Adsorption on Erdős–Rényi Random Graphs

AU - Dhara, S.

AU - van Leeuwaarden, J.S.H.

AU - Mukherjee, D.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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.

AB - 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.

KW - Frequency assignment

KW - Greedy independent set

KW - Jamming limit

KW - Parking problem

KW - Random graphs

KW - Random sequential adsorption

UR - http://www.scopus.com/inward/record.url?scp=84979289573&partnerID=8YFLogxK

U2 - 10.1007/s10955-016-1583-z

DO - 10.1007/s10955-016-1583-z

M3 - Article

VL - 164

SP - 1217

EP - 1232

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5

ER -