Related papers: On protected nodes in Digital Search Trees
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 present approximation algorithms for the following NP-hard optimization problems related to bottleneck spanning trees in metric spaces. 1. The disjoint bottleneck spanning tree problem: Given $n$ pairs of points in a metric space, find…
We study the extreme local structure of plane binary trees through the distribution of leaves at maximum depth. We first address two basic questions: (i) the asymptotic probability that exactly two leaves occur at the deepest level, and…
We focus on the average-case analysis: A function w : V -> Z+ is given which defines the likelihood for a node to be the one marked, and we want the strategy that minimizes the expected number of queries. Prior to this paper, very little…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…
Tree-based networks are a class of phylogenetic networks that attempt to formally capture what is meant by "tree-like" evolution. A given non-tree-based phylogenetic network, however, might appear to be very close to being tree-based, or…
We explore a generating function trick which allows us to keep track of infinitely many statistics using finitely many variables, by recording their individual distributions rather than their joint distributions. Building on previous work…
We study the distribution of fringe trees in Patricia tries (extending earlier results by Ischebeck (2025)) and compressed binary search trees; both cases are random binary trees that have been compressed by deleting nodes of outdegree 1 so…
A fringe subtree of a rooted tree is a subtree consisting of one of the nodes and all its descendants. In this paper, we are specifically interested in the number of non-isomorphic trees that appear in the collection of all fringe subtrees…
We study the following problem that is motivated by demand-aware network design: Given a tree~$G$, the task is to find a binary tree~$H$ on the same vertex set. The objective is to minimize the sum of distances in~$H$ between vertex pairs…
Rotation distance between rooted binary trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. We give an efficient,…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
We present an approach to match partially occluded plant leaves with databases of full plant leaves. Although contour based 2D shape matching has been studied extensively in the last couple of decades, matching occluded leaves with full…
Rooted phylogenetic networks allow biologists to represent evolutionary relationships between present-day species by revealing ancestral speciation and hybridization events. A convenient and well-studied class of such networks are…
Thin spanning trees lie at the intersection of graph theory, approximation algorithms, and combinatorial optimization. They are central to the long-standing \emph{thin tree conjecture}, which asks whether every $k$-edge-connected graph…
Demand-aware communication networks are networks whose topology is optimized toward the traffic they need to serve. These networks have recently been enabled by novel optical communication technologies and are investigated intensively in…
The k-d tree is a classic binary space-partitioning tree used to organize points in k-dimensional space. While used in computational geometry and graphics, the data structure has a long history of application in nearest neighbor search. The…
The k-d tree was one of the first spatial data structures proposed for nearest neighbor search. Its efficacy is diminished in high-dimensional spaces, but several variants, with randomization and overlapping cells, have proved to be…
Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…