Related papers: Randomized Incremental Construction of Net-Trees
We study the growth of a time-ordered rooted tree by probabilistic attachment of new vertices to leaves. We construct a likelihood function of the leaves based on the connectivity of the tree. We take such connectivity to be induced by the…
We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of…
We propose a new arithmetic for non-empty rooted unordered trees simply called trees. After discussing tree representation and enumeration, we define the operations of tree addition, multiplication and stretch, prove their properties, and…
A data structure, called a biased range tree, is presented that preprocesses a set S of n points in R^2 and a query distribution D for 2-sided orthogonal range counting queries. The expected query time for this data structure, when queries…
We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree…
Random forests on the one hand, and neural networks on the other hand, have met great success in the machine learning community for their predictive performance. Combinations of both have been proposed in the literature, notably leading to…
In this paper we describe an algorithm that embeds a graph metric $(V,d_G)$ on an undirected weighted graph $G=(V,E)$ into a distribution of tree metrics $(T,D_T)$ such that for every pair $u,v\in V$, $d_G(u,v)\leq d_T(u,v)$ and…
A treap is a classic randomized binary search tree data structure that is easy to implement and supports O(\log n) expected time access. However, classic treaps do not take advantage of the input distribution or patterns in the input. Given…
We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…
We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…
We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated…
Supertree construction is the process by which a set of phylogenetic trees, each on a subset of the overall set X of species, is combined into a tree on the full set S. The traditional use of supertree methods is the assembly of a large…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
In this paper, we consider the problem of reconstructing trees from traces in the tree edit distance model. Previous work by Davies et al. (2019) analyzed special cases of reconstructing labeled trees. In this work, we significantly expand…
We introduce the notion of t-restricted doubling dimension of a point set in Euclidean space as the local intrinsic dimension up to scale t. In many applications information is only relevant for a fixed range of scales. We present an…
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of…
\begin{abstract} Greedy permutations, also known as Gonzalez Orderings or Farthest Point Traversals are a standard way to approximate $k$-center clustering and have many applications in sampling and approximating metric spaces. A greedy…
Random Forests are one of the most popular classifiers in machine learning. The larger they are, the more precise is the outcome of their predictions. However, this comes at a cost: their running time for classification grows linearly with…
Industrial robots can solve very complex tasks in controlled environments, but modern applications require robots able to operate in unpredictable surroundings as well. An increasingly popular reactive policy architecture in robotics is…
Phylogenetic networks are used to represent the evolutionary history of species. Recently, the new class of orchard networks was introduced, which were later shown to be interpretable as trees with additional horizontal arcs. This makes the…