The jamming constant of uniform random graphs

Paola Bermolen, Matthieu Jonckheere and Pascal Moyal

Stochastic Processes and their Applications, 2017, vol. 127, issue 7, 2138-2178

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.

Keywords: Random graph; Configuration model; Parking process; Measure-valued Markov process; Hydrodynamic limit (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2016.10.005

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