Long and short paths in uniform random recursive dags |
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Authors: | Luc Devroye Svante Janson |
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Institution: | 1.School of Computer Science,McGill University,Montreal,Canada;2.Department of Mathematics,Uppsala University,Uppsala,Sweden |
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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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Keywords: | |
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