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Long and short paths in uniform random recursive dags
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2011 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 49, no 1, 61-77 p.Article in journal (Refereed) Published
Abstract [en]

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 sigma such that S (n) /log n ->sigma in probability as n -> a. We also show that max (1a parts per thousand currency signia parts per thousand currency signn) S (i) /log n ->sigma in probability.

Place, publisher, year, edition, pages
2011. Vol. 49, no 1, 61-77 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-150683DOI: 10.1007/s11512-009-0118-0ISI: 000288019500004OAI: oai:DiVA.org:uu-150683DiVA: diva2:408243
Available from: 2011-04-04 Created: 2011-04-04 Last updated: 2017-12-11Bibliographically approved

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