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April 2011 Long and short paths in uniform random recursive dags
Luc Devroye, Svante Janson
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Ark. Mat. 49(1): 61-77 (April 2011). DOI: 10.1007/s11512-009-0118-0

Abstract

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.

Funding Statement

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.

Citation

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Luc Devroye. Svante Janson. "Long and short paths in uniform random recursive dags." Ark. Mat. 49 (1) 61 - 77, April 2011. https://doi.org/10.1007/s11512-009-0118-0

Information

Received: 1 June 2009; Published: April 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1230.60092
MathSciNet: MR2784257
Digital Object Identifier: 10.1007/s11512-009-0118-0

Rights: 2010 © Institut Mittag-Leffler

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Vol.49 • No. 1 • April 2011
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