Related papers: Odds-On Trees
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
We show an $\widetilde{O}(m^{1.5} \epsilon^{-1})$ time algorithm that on a graph with $m$ edges and $n$ vertices outputs its spanning tree count up to a multiplicative $(1+\epsilon)$ factor with high probability, improving on the previous…
We consider the problem of searching for an object on a line at an unknown distance OPT from the original position of the searcher, in the presence of a cost of d for each time the searcher changes direction. This is a generalization of the…
Approximate nearest-neighbor search is a fundamental algorithmic problem that continues to inspire study due its essential role in numerous contexts. In contrast to most prior work, which has focused on point sets, we consider…
Crystal structure prediction has been a subject of topical interest, but remains a substantial challenge, especially for complex structures as it deals with the global minimization of the extremely rugged high-dimensional potential energy…
Let $T$ be a tree space (or tree network) represented by a weighted tree with $t$ vertices, and $S$ be a set of $n$ stochastic points in $T$, each of which has a fixed location with an independent existence probability. We investigate two…
Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or…
The palindromic tree (a.k.a. eertree) for a string $S$ of length $n$ is a tree-like data structure that represents the set of all distinct palindromic substrings of $S$, using $O(n)$ space [Rubinchik and Shur, 2018]. It is known that, when…
We propose a new method for estimating the number of answers OUT of a small join query Q in a large database D, and for uniform sampling over joins. Our method is the first to satisfy all the following statements. - Support arbitrary Q,…
We present a randomized algorithm for reconstructing directed rooted trees of $n$ nodes and node degree at most $d$, by asking at most $O(dn\log^2 n)$ path queries. Each path query takes as input an origin node and a target node, and…
The value of an American option is the maximized value of the discounted cash flows from the option. At each time step, one needs to compare the immediate exercise value with the continuation value and decide to exercise as soon as the…
We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated…
This thesis presents analysis of the properties and run-time of the Rapidly-exploring Random Tree (RRT) algorithm. It is shown that the time for the RRT with stepsize $\epsilon$ to grow close to every point in the $d$-dimensional unit cube…
A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More…
This paper describes experiments, on two domains, to investigate the effect of averaging over predictions of multiple decision trees, instead of using a single tree. Other authors have pointed out theoretical and commonsense reasons for…
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…
Decision trees are widely adopted machine learning models due to their simplicity and explainability. However, as training data size grows, standard methods become increasingly slow, scaling polynomially with the number of training…
The skyline of a set $P$ of points ($SKY(P)$) consists of the "best" points with respect to minimization or maximization of the attribute values. A point $p$ dominates another point $q$ if $p$ is as good as $q$ in all dimensions and it is…
We construct near optimal linear decision trees for a variety of decision problems in combinatorics and discrete geometry. For example, for any constant $k$, we construct linear decision trees that solve the $k$-SUM problem on $n$ elements…
In the polytope membership problem, a convex polytope $K$ in $\mathbb{R}^d$ is given, and the objective is to preprocess $K$ into a data structure so that, given any query point $q \in \mathbb{R}^d$, it is possible to determine efficiently…