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We provide a fast distributed algorithm for detecting $h$-cycles in the \textsf{Congested Clique} model, whose running time decreases as the number of $h$-cycles in the graph increases. In undirected graphs, constant-round algorithms are…
Given a large dataset of binary codes and a binary query point, we address how to efficiently find $K$ codes in the dataset that yield the largest cosine similarities to the query. The straightforward answer to this problem is to compare…
We consider the fundamental problem of detecting/counting copies of a fixed pattern graph in a host graph. The recent progress on this problem has not included complete pattern graphs, i.e., cliques (and their complements, i.e., edge-free…
The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…
We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…
Inspired by the classical fractional cascading technique, we introduce new techniques to speed up the following type of iterated search in 3D: The input is a graph $\mathbf{G}$ with bounded degree together with a set $H_v$ of 3D hyperplanes…
Density peaks clustering has become a nova of clustering algorithm because of its simplicity and practicality. However, there is one main drawback: it is time-consuming due to its high computational complexity. Herein, a density peaks…
In recent years, deep neural networks have had great success in machine learning and pattern recognition. Architecture size for a neural network contributes significantly to the success of any neural network. In this study, we optimize the…
Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm that enable us to explore the high order statistics efficiently in large data sets. Central to this technique is to make decomposition both of fields and…
Most decision and optimization problems encountered in practice fall into one of two categories with respect to any particular solving method or algorithm: either the problem is solved quickly (easy) or else demands an impractically long…
We propose a fast and accurate 6D object pose estimation from a RGB-D image. Our proposed method is template matching based and consists of three main technical components, PCOF-MOD (multimodal PCOF), balanced pose tree (BPT) and optimum…
Recently, a new method for encoding data sets in the form of "Density Codes" was proposed in the literature (Courrieu, 2006). This method allows to compare sets of points belonging to every multidimensional space, and to build shape spaces…
Prior methods for retrieval of nearest neighbors in high dimensions are fast and approximate--providing probabilistic guarantees of returning the correct answer--or slow and exact performing an exhaustive search. We present Certified…
Parametric search has been widely used in geometric algorithms. Cole's improvement provides a way of saving a logarithmic factor in the running time over what is achievable using the standard method. Unfortunately, this improvement comes at…
Cosmological measurements require the calculation of nontrivial quantities over large datasets. The next generation of survey telescopes (such as DES, PanSTARRS, and LSST) will yield measurements of billions of galaxies. The scale of these…
We propose theoretical and empirical improvements for two-stage hashing methods. We first provide a theoretical analysis on the quality of the binary codes and show that, under mild assumptions, a residual learning scheme can construct…
A popular paradigm for 3D point cloud registration is by extracting 3D keypoint correspondences, then estimating the registration function from the correspondences using a robust algorithm. However, many existing 3D keypoint techniques tend…
We present a new algorithm to rapidly compute the two-point (2PCF), three-point (3PCF) and n-point (n-PCF) correlation functions in roughly O(N log N) time for N particles, instead of O(N^n) as required by brute force approaches. The…
The paper presents an algorithm for depth map estimation from the light field images in relatively small amount of time, using only single thread on CPU. The proposed method improves existing principle of line fitting in 4-dimensional light…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…