Related papers: Continuous time digital search tree and a border a…
We consider a general class of branching processes in discrete time, where particles have types belonging to a Polish space and reproduce independently according to their type. If the process is critical and the mean distribution of types…
We consider a multi-level aggregation problem in a weighted rooted tree, studied recently by Bienkowski et al. (2015). In this problem requests arrive over time at the nodes of the tree, and each request specifies a deadline. A request is…
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 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 focus of this paper is the analysis of real-time systems with recursion, through the development of good theoretical techniques which are implementable. Time is modeled using clock variables, and recursion using stacks. Our technique…
The present paper is devoted to estimating the speed of convergence towards consensus for a general class of discrete-time multi-agent systems. In the systems considered here, both the topology of the interconnection graph and the weight of…
In the critical beta-splitting model of a random $n$-leaf binary tree, leaf-sets are recursively split into subsets, and a set of $m$ leaves is split into subsets containing $i$ and $m-i$ leaves with probabilities proportional to…
Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…
We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle…
Connectivity query processing is a fundamental problem in graph processing. Given an undirected graph and two query vertices, the problem aims to identify whether they are connected via a path. Given frequent edge updates in real graph…
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…
Motivated by the study of random temporal networks, we introduce a class of random trees that we coin \emph{uniform temporal trees}. A uniform temporal tree is obtained by assigning independent uniform $[0,1]$ labels to the edges of a…
Geolocated time series, i.e., time series associated with certain locations, abound in many modern applications. In this paper, we consider hybrid queries for retrieving geolocated time series based on filters that combine spatial distance…
Many real world networks are considered temporal networks, in which the chronological ordering of the edges has importance to the meaning of the data. Performing temporal subgraph matching on such graphs requires the edges in the subgraphs…
Frequent tree mining asks us to enumerate tree patterns that occur frequently in a database of rooted trees. This problem is motivated by tree-structured data in bioinformatics, such as glycans and pseudoknot-free RNA secondary structures.…
We study the problem of collective tree exploration in which a team of $k$ mobile agents must collectively visit all nodes of an unknown tree in as few moves as possible. The agents all start from the root and discover adjacent edges as…
Identifying communities from temporal networks facilitates the understanding of potential dynamic relationships among entities, which has already received extensive applications. However, existing methods primarily rely on lower-order…
When the focus is on the relationships or interactions between entities, graphs offer an intuitive model for many real-world data. Such graphs are usually large and change over time, thus, requiring models and strategies that explore their…
We introduce generalizations of Aldous' Brownian Continuous Random Tree as scaling limits for multicritical models of discrete trees. These discrete models involve trees with fine-tuned vertex-dependent weights ensuring a k-th root…
We study the statistics of height and balanced height in the binary search tree problem in computer science. The search tree problem is first mapped to a fragmentation problem which is then further mapped to a modified directed polymer…