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We show that every n-point tree metric admits a (1+eps)-embedding into a C(eps) log n-dimensional L_1 space, for every eps > 0, where C(eps) = O((1/eps)^4 log(1/eps)). This matches the natural volume lower bound up to a factor depending…

Predicting the nodes of a given graph is a fascinating theoretical problem with applications in several domains. Since graph sparsification via spanning trees retains enough information while making the task much easier, trees are an…

A labeled tree (or a trie) is a natural generalization of a string, which can also be seen as a compact representation of a set of strings. This paper considers the labeled tree indexing problem, and provides a number of new results on…

We consider the problem of implementing a space-efficient dynamic trie, with an emphasis on good practical performance. For a trie with $n$ nodes with an alphabet of size $\sigma$, the information-theoretic lower bound is $n \log \sigma +…

This paper presents a detailed comparison of a recently proposed algorithm for optimizing decision trees, tree alternating optimization (TAO), with other popular, established algorithms. We compare their performance on a number of…

Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the problem of counting inversions in arrays originated in mathematical…

We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…

Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…

The early development of a zygote can be mathematically described by a developmental tree. To compare developmental trees of different species, we need to define distances on trees. If children cells after a division are not…

This paper deals with the size of the spanning tree of p randomly chosen nodes in a binary search tree. It is shown via generating functions methods, that for fixed p, the (normalized) spanning tree size converges in law to the Normal…

Phylogenetic trees represent evolutionary relationships among sets of organisms. Popular phylogenetic reconstruction approaches typically yield hundreds to thousands of trees on a common leafset. Storing and sharing such large collection of…

For a set $P$ of $n$ points in the plane in general position, a non-crossing spanning tree is a spanning tree of the points where every edge is a straight-line segment between a pair of points and no two edges intersect except at a common…

An ancestry labeling scheme assigns labels (bit strings) to the nodes of rooted trees such that ancestry queries between any two nodes in a tree can be answered merely by looking at their corresponding labels. The quality of an ancestry…

We propose BS-tree, an in-memory implementation of the B+-tree that adopts the structure of the disk-based index (i.e., a balanced, multiway tree), setting the node size to a memory block that can be processed fast and in parallel using…

A uniform recursive tree on $n$ vertices is a random tree where each possible $(n-1)!$ labeled recursive rooted tree is selected with equal probability. In this paper we introduce and study weighted trees, a non-uniform recursive tree model…

Conventionally, random forests are built from "greedy" decision trees which each consider only one split at a time during their construction. The sub-optimality of greedy implementation has been well-known, yet mainstream adoption of more…

We present sparse tree-based and list-based density estimation methods for binary/categorical data. Our density estimation models are higher dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the…

We provide an $O(n \log n)$ algorithm computing the linear maximum induced matching width of a tree and an optimal layout.

In this paper, we study learning and testing decision tree of size and depth that are significantly smaller than the number of attributes $n$. Our main result addresses the problem of poly$(n,1/\epsilon)$ time algorithms with…

In the $k$-dispersion problem, we need to select $k$ nodes of a given graph so as to maximize the minimum distance between any two chosen nodes. This can be seen as a generalization of the independent set problem, where the goal is to…