Related papers: A fast recursive coordinate bisection tree for nei…
Similarity graphs are an active research direction for the nearest neighbor search (NNS) problem. New algorithms for similarity graph construction are continuously being proposed and analyzed by both theoreticians and practitioners.…
Consider the following generalization of the classic binary search problem: a searcher is required to find a hidden vertex $x$ in a tree $T$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$. After…
In many situations, the choice of an adequate similarity measure or metric on the feature space dramatically determines the performance of machine learning methods. Building automatically such measures is the specific purpose of…
In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a…
We present a new C++ code for collisional N-body simulations of star clusters. The code uses the Hermite fourth-order scheme with block time steps, for advancing the particles in time, while the forces and neighboring particles are computed…
Contemporary accelerator designs exhibit a high degree of spatial localization, wherein two-dimensional physical distance determines communication costs between processing elements. This situation presents considerable algorithmic…
Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…
Given a text, rank and select queries return the number of occurrences of a character up to a position (rank) or the position of a character with a given rank (select). These queries have applications in, e.g., compression, computational…
We provide a new set of on-shell recursion relations for tree-level scattering amplitudes, which are valid for any non-trivial theory of massless particles. In particular, we reconstruct the scattering amplitudes from (a subset of) their…
Pre-transformed polar codes (PTPCs) form a class of codes that perform close to the finite-length capacity bounds. The minimum distance and the number of minimum weight codewords are two decisive properties for their performance. In this…
Given a collection of points in R^3, KD-Tree and R-Tree are well-known nearest neighbor search (NNS) algorithms that rely on space partitioning and spatial indexing techniques. However, when the query point is far from the data points or…
We develop combinatorial methods for computing the rotation distance between binary trees, i.e., equivalently, the flip distance between triangulations of a polygon. As an application, we prove that, for each n, there exist size n trees at…
In this paper we describe an adaptive softening length formalism for collisionless N-body and self-gravitating Smoothed Particle Hydrodynamics (SPH) calculations which conserves momentum and energy exactly. This means that spatially…
With the widespread use of self-consistent field methods, including Hartree-Fock and Density Functional Theory, the implications of accelerating these methods are immense. To this end, we develop a tensor hypercontraction construction with…
In particle simulations, the weights of particles determine how many physical particles they represent. Adaptively adjusting these weights can greatly improve the efficiency of the simulation, without creating severe nonphysical artifacts.…
The working-set bound [Sleator and Tarjan, J. ACM, 1985] roughly states that searching for an element is fast if the element was accessed recently. Binary search trees, such as splay trees, can achieve this property in the amortized sense,…
Nearest neighbor search is a very active field in machine learning for it appears in many application cases, including classification and object retrieval. In its canonical version, the complexity of the search is linear with both the…
Between the leaves and the nodes of a complete binary tree, a separate parent-child-sister hierarchy is employed independent of the parent-child-sister hierarchy used for the rest of the tree. Two different versions of such a local…
In this paper, we introduce a new representation for ordered trees, the weight sequence representation. We then use this to construct new representations for both rooted trees and free trees, namely the canonical weight sequence…
Binary codes are widely used to represent the data due to their small storage and efficient computation. However, there exists an ambiguity problem that lots of binary codes share the same Hamming distance to a query. To alleviate the…