The height of depth‐weighted random recursive trees

In this paper, we introduce a model of depth‐weighted random recursive trees, created by recursively joining a new leaf to an existing vertex v. In this model, the probability of choosing v depends on its depth in the tree. In particular, we assume that there is a function f such that if v has depth...

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Bibliographic Details
Published inRandom structures & algorithms Vol. 56; no. 3; pp. 851 - 866
Main Authors Leckey, Kevin, Mitsche, Dieter, Wormald, Nick
Format Journal Article
LanguageEnglish
Published New York John Wiley & Sons, Inc 01.05.2020
Wiley Subscription Services, Inc
Wiley
Subjects
height
Mathematics
random recursive trees
random trees
Trees
Trees (mathematics)
random recursive trees
random trees
height
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Summary:In this paper, we introduce a model of depth‐weighted random recursive trees, created by recursively joining a new leaf to an existing vertex v. In this model, the probability of choosing v depends on its depth in the tree. In particular, we assume that there is a function f such that if v has depth k then its probability of being chosen is proportional to f(k). We consider the expected value of the diameter of this model as determined by f, and for various increasing f we find expectations that range from polylogarithmic to linear.
Bibliography:Part of this research was done while the second and third authors were in residence at Centre Recerca Matemàtica (CRM) during the program “Strategic Behavior and Phase Transitions in Random and Complex Combinatorial Structures” (April‐June 2015).
ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20901