Related papers: Compaction for two models of logarithmic-depth tre…
This paper provides a unifying framework for a range of categorical constructions characterised by universal mapping properties, within the realm of compactifications of discrete structures. Some classic examples fit within this broad…
In SODA'99, Chan introduced a simple type of planar straight-line upward order-preserving drawings of binary trees, known as LR drawings: such a drawing is obtained by picking a root-to-leaf path, drawing the path as a straight line, and…
In this paper, we redesign and simplify an algorithm due to Remy et al. for the generation of rooted planar trees that satisfies a given partition of degrees. This new version is now optimal in terms of random bit complexity, up to a…
Obtaining accurate and well calibrated probability estimates from classifiers is useful in many applications, for example, when minimising the expected cost of classifications. Existing methods of calibrating probability estimates are…
We present an algorithm for computing a maximum agreement subtree of two unrooted evolutionary trees. It takes O(n^{1.5} log n) time for trees with unbounded degrees, matching the best known time complexity for the rooted case. Our…
Following Poupard's study of strictly ordered binary trees with respect to two parameters, namely, "end of minimal chain" and "parent of maximum leaf" a true Tree Calculus is being developed to solve a partial difference equation system and…
In binary and ordinal regression one can distinguish between a location component and a scaling component. While the former determines the location within the range of the response categories, the scaling indicates variance heterogeneity.…
Given a set S of n \geq d points in general position in R^d, a random hyperplane split is obtained by sampling d points uniformly at random without replacement from S and splitting based on their affine hull. A random hyperplane search tree…
In this study, we address the problem of compacting Church numerals. Church numerals appear as a representation of the repetitive part of data in higher-order compression. We propose a novel decomposition scheme for a natural number using…
In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively (from the root) split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities…
In this work we introduce and study various generalizations of the notion of increasingly labelled trees, where the label of a child node is always larger than the label of its parent node, to multilabelled tree families, where the nodes in…
Among subgraphs with a fixed number of vertices of the regular square lattice, we prove inequalities that essentially say that those with smaller boundaries have larger numbers of spanning trees and vice-versa. As an application, we relate…
The Yule-Harding-Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model are two binary tree generating models that are widely used in evolutionary biology. Understanding the distributions of clade sizes under…
Log-structured merge (LSM) trees offer efficient ingestion by appending incoming data, and thus, are widely used as the storage layer of production NoSQL data stores. To enable competitive read performance, LSM-trees periodically…
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a…
Recursive partitioning is the core of several statistical methods including CART, random forest, and boosted trees. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a…
We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional "doubling events" when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
The alpha model, a parametrized family of probabilities on cladograms (rooted binary leaf labeled trees), is introduced. This model is Markovian self-similar, deletion-stable (sampling consistent), and passes through the Yule, Uniform and…