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Long and short paths in uniform random recursive dags

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Arkiv för Matematik

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 S n is the shortest path distance from node n to the root, then we determine the constant σ such that S n /log n→σ in probability as n→∞. We also show that max 1≤i≤n S i /log n→σ in probability.

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Author information

Authors and Affiliations

  1. School of Computer Science, McGill University, 3450 University Street, Montreal, QC, H3A 2K6, Canada

    Luc Devroye

  2. Department of Mathematics, Uppsala University, P.O. Box 480, SE-751 06, Uppsala, Sweden

    Svante Janson

Authors
  1. Luc Devroye
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  2. Svante Janson
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Correspondence to Svante Janson.

Additional information

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

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  • DOI: https://doi.org/10.1007/s11512-009-0118-0

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