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The jamming constant of uniform random graphs

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  • Bermolen, Paola
  • Jonckheere, Matthieu
  • Moyal, Pascal

Abstract

By constructing jointly a random graph and an associated exploration process, we define the dynamics of a “parking process” on a class of uniform random graphs as a measure-valued Markov process, representing the empirical degree distribution of non-explored nodes. We then establish a functional law of large numbers for this process as the number of vertices grows to infinity, allowing us to assess the jamming constant of the considered random graphs, i.e. the size of the maximal independent set discovered by the exploration algorithm. This technique, which can be applied to any uniform random graph with a given–possibly unbounded–degree distribution, can be seen as a generalization in the space of measures, of the differential equation method introduced by Wormald.

Suggested Citation

  • Bermolen, Paola & Jonckheere, Matthieu & Moyal, Pascal, 2017. "The jamming constant of uniform random graphs," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2138-2178.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:7:p:2138-2178
    DOI: 10.1016/j.spa.2016.10.005
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    References listed on IDEAS

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    1. Ferrari, Pablo A. & Fernández, Roberto & Garcia, Nancy L., 2002. "Perfect simulation for interacting point processes, loss networks and Ising models," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 63-88, November.
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    Cited by:

    1. Mohamed Habib Aliou Diallo Aoudi & Pascal Moyal & Vincent Robin, 2022. "Markovian Online Matching Algorithms on Large Bipartite Random Graphs," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3195-3225, December.
    2. Jonckheere, Matthieu & Sáenz, Manuel, 2021. "Asymptotic optimality of degree-greedy discovering of independent sets in Configuration Model graphs," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 122-150.

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