Arkiv för Matematik

Long and short paths in uniform random recursive dags

Luc Devroye and Svante Janson

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In a uniform random recursive k-directed acyclic graph, there is a root, 0, and each node in turn, from 1 to n, chooses k uniform random parents from among the nodes of smaller index. If Sn is the shortest path distance from node n to the root, then we determine the constant σ such that Sn/log nσ in probability as n→∞. We also show that max 1≤inSi/log nσ in probability.


L. Devroye’s research was sponsored by NSERC Grant A3456. The research was mostly done at the Institute Mittag-Leffler during the programme Discrete Probability held in 2009.

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Ark. Mat., Volume 49, Number 1 (2011), 61-77.

Received: 1 June 2009
First available in Project Euclid: 31 January 2017

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2010 © Institut Mittag-Leffler


Devroye, Luc; Janson, Svante. Long and short paths in uniform random recursive dags. Ark. Mat. 49 (2011), no. 1, 61--77. doi:10.1007/s11512-009-0118-0.

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