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We study the random m-ary search tree model (where m stands for the number of branches of a search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain…
We study the space requirement of $m$-ary search trees under the random permutation model when $m \geq 27$ is fixed. Chauvin and Pouyanne have shown recently that $X_n$, the space requirement of an $m$-ary search tree on $n$ keys, equals…
We derive asymptotics of moments and identify limiting distributions, under the random permutation model on m-ary search trees, for functionals that satisfy recurrence relations of a simple additive form. Many important functionals…
We revisit the random $m$-ary search tree and study a finer profile of its node outdegrees with the purpose of exploring possibilities of data structure compression. The analysis is done via P\'olya urns. The analysis shows that the number…
The space requirements of an $m$-ary search tree satisfies a well-known phase transition: when $m\leq 26$, the second order asymptotics is Gaussian. When $m\geq 27$, it is not Gaussian any longer and a limit $W$ of a complex-valued…
Consider a random recusive tree with n vertices. We show that the number of vertices with even depth is asymptotically normal as n tends to infinty. The same is true for the number of vertices of depth divisible by m for m=3, 4 or 5; in all…
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…
We study the size and the external path length of random tries and show that they are asymptotically independent in the asymmetric case but strongly dependent with small periodic fluctuations in the symmetric case. Such an unexpected…
Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such an analysis for several shape parameters on random symmetric…
This survey studies asymptotics of random fringe trees and extended fringe trees in random trees that can be constructed as family trees of a Crump-Mode-Jagers branching process, stopped at a suitable time. This includes random recursive…
Search trees are fundamental data structures in computer science. We study functionals on random search trees that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal…
We study fringe subtrees of random $ m $-ary search trees and of preferential attachment trees, by putting them in the context of generalised P\'olya urns. In particular we show that for the random $ m $-ary search trees with $ m\leq 26 $…
We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the…
A relaxed $k$-ary tree is an ordered directed acyclic graph with a unique source and sink in which every node has out-degree $k$. These objects arise in the compression of trees in which some repeated subtrees are factored and repeated…
We study the asymptotics of the $p$-mapping model of random mappings on $[n]$ as $n$ gets large, under a large class of asymptotic regimes for the underlying distribution $p$. We encode these random mappings in random walks which are shown…
We study the asymptotic behavior of the maximum degree in the evolving tree model with a choice based on both degree and fitness of a vertex. The tree is constructed in the following recursive way. Each vertex is assigned a parameter to it…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
We study protected nodes in $m$-ary search trees, by putting them in context of generalised P\'olya urns. We show that the number of two-protected nodes (the nodes that are neither leaves nor parents of leaves) in a random ternary search…
We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…
In this paper we study a variation of the accessibility percolation model, this is also motivated by evolutionary biology and evolutionary computation. Consider a tree whose vertices are labeled with random numbers. We study the probability…