相关论文: Understanding Search Trees via Statistical Physics

We study the number of random records in an arbitrary split tree (or equivalently, the number of random cuttings required to eliminate the tree). We show that a classical limit theorem for convergence of sums of triangular arrays to…

We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…

We investigate the genealogical structure of general critical or subcritical continuous-state branching processes. Analogously to the coding of a discrete tree by its contour function, this genealogical structure is coded by a real-valued…

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…

This paper is a variation on the uniform spanning tree theme. We use random spanning forests to solve the following problem: for a Markov process on a finite set of size $n$, find a probability law on the subsets of any given size $m \leq…

We study the detection error probabilities associated with an M-ary relay tree, where the leaves of the tree correspond to identical and independent sensors. Only these leaves are sensors. The root of the tree represents a fusion center…

The rooted tree is an important data structure, and the subtree size, height, and depth are naturally defined attributes of every node. We consider the problem of the existence of a k-ary tree given a list of attribute sequences. We give…

We study the parking process on the random recursive tree. We first prove that although the random recursive tree has a non-degenerate Benjamini--Schramm limit, the phase transition for the parking process appears at density $0$. We then…

As a flexible nonparametric learning tool, the random forests algorithm has been widely applied to various real applications with appealing empirical performance, even in the presence of high-dimensional feature space. Unveiling the…

We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…

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…

Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…

We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…

Consider a tree network T, where each edge acts as an independent copy of a given channel M, and information is propagated from the root. For which T and M does the configuration obtained at level n of T typically contain significant…

A novel and powerful method is presented for the study of rare switching events in complex systems with multiscale energy landscapes. The method performs an umbrella sampling of the equilibrium distribution of the system in hyperplanes…

We use the traveling front approach to derive exact asymptotic results for the statistics of the number of particles in a class of directed diffusion limited aggregation models on a Cayley tree. We point out that some aspects of these…

The Temporal Graph Exploration problem (TEXP) takes as input a temporal graph, i.e., a sequence of graphs $(G_i)_{i\in \mathbb{N}}$ on the same vertex set, and asks for a walk of shortest length visiting all vertices, where the $i$-th step…

We consider a discrete-time dynamical process on graphs, firstly introduced in connection with a protocol for controlling large networks of spin 1/2 quantum mechanical particles [Phys. Rev. Lett. 99, 100501 (2007)]. A description is as…

We analyze a class of spatial random spanning trees built on a realization of a homogeneous Poisson point process of the plane. This tree has a simple radial structure with the origin as its root. We first use stochastic geometry arguments…