Related papers: Building a Balanced k-d Tree in O(kn log n) Time

In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…

In this paper we propose an online approximate k-nn graph building algorithm, which is able to quickly update a k-nn graph using a flow of data points. One very important step of the algorithm consists in using the current distributed graph…

We give an algorithm to compute all the local peaks in the $k$-level of an arrangement of $n$ lines in $O(n \log n) + \tilde{O}((kn)^{2/3})$ time. We can also find $\tau$ largest peaks in $O(n \log ^2 n) + \tilde{O}((\tau n)^{2/3})$ time.…

In this paper, we introduce a collaborative training algorithm of balanced random forests with convolutional neural networks for domain adaptation tasks. In real scenarios, most domain adaptation algorithms face the challenges from noisy,…

In this paper, we design parallel write-efficient geometric algorithms that perform asymptotically fewer writes than standard algorithms for the same problem. This is motivated by emerging non-volatile memory technologies with read…

A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary…

We consider the $k$-center problem in which the centers are constrained to lie on two lines. Given a set of $n$ weighted points in the plane, we want to locate up to $k$ centers on two parallel lines. We present an $O(n\log^2 n)$ time…

Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…

We propose a transformer architecture and training strategy for tree generation. The architecture processes data at multiple resolutions and has an hourglass shape, with middle layers processing fewer tokens than outer layers. Similar to…

Decision trees have been studied extensively in the context of fairness, aiming to maximize prediction performance while ensuring non-discrimination against different groups. Techniques in this space usually focus on imposing constraints at…

Decision trees are an extremely popular machine learning technique. Unfortunately, overfitting in decision trees still remains an open issue that sometimes prevents achieving good performance. In this work, we present a novel approach for…

Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees.…

We consider the problem of augmenting an $n$-vertex tree with one shortcut in order to minimize the diameter of the resulting graph. The tree is embedded in an unknown space and we have access to an oracle that, when queried on a pair of…

We show that the cophylogenetic distance, k-interval cospeciation, is distinct from other metrics and accounts for global congruence between locally incongruent trees. The growth of the neighborhood of trees which satisfy the largest…

The tree inclusion problem is, given two node-labeled trees $P$ and $T$ (the ``pattern tree'' and the ``target tree''), to locate every minimal subtree in $T$ (if any) that can be obtained by applying a sequence of node insertion operations…

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…

Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…

We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…

Manipulating downward-closed sets of vectors forms the basis of so-called antichain-based algorithms in verification. In that context, the dimension of the vectors is intimately tied to the size of the input structure to be verified. In…

In this paper we provide faster algorithms for solving the geometric median problem: given $n$ points in $\mathbb{R}^{d}$ compute a point that minimizes the sum of Euclidean distances to the points. This is one of the oldest non-trivial…