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In this article, we propose a numerical method to solve semi-discrete optimal transport problems for gigantic pointsets (108 points and more). By pushing the limits by several orders of magnitude, it opens the path to new applications in…
In this paper, we consider the problem of covering a plane region with unit discs. We present an improved upper bound and the first nontrivial lower bound on the number of discs needed for such a covering, depending on the area and…
Neighborhood construction models are important in finding connection among the data points, which helps demonstrate interrelations among the information. Hence, employing a new approach to find neighborhood among the data points is a…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
Preparing high-quality datasets required by various data-driven AI and machine learning models has become a cornerstone task in data-driven analysis. Conventional data discovery methods typically integrate datasets towards a single…
Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…
We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. The framework is sufficiently general to support diagrams embedded on a family of two-dimensional…
We develop an algorithm for i) computing generalized regular $k$-point grids, ii) reducing the grids to their symmetrically distinct points, and iii) mapping the reduced grid points into the Brillouin zone. The algorithm exploits the…
The $k$ nearest neighbor ($k$NN) query is a fundamental problem in databases. Given a set of multidimensional data points and a query point, $k$NN returns the $k$ nearest neighbors based on a scoring function such as weighted sum given an…
An efficient computer algorithm is described for the perspective drawing of a wide class of surfaces. The class includes surfaces corresponding lo single-valued, continuous functions which are defined over rectangular domains. The algorithm…
We describe the development of a new software tool, called "Pomelo", for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to…
Bipartite graphs, modeling relationships between two types of entities, are widely used in practical applications. Community search, a fundamental problem in bipartite graphs, has gained significant attention. However, existing studies…
Many web databases are "hidden" behind proprietary search interfaces that enforce the top-$k$ output constraint, i.e., each query returns at most $k$ of all matching tuples, preferentially selected and returned according to a proprietary…
In this work we present in-network techniques to improve the efficiency of spatial aggregate queries. Such queries are very common in a sensornet setting, demanding more targeted techniques for their handling. Our approach constructs and…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
Scientific endeavors such as large astronomical surveys generate databases on the terabyte scale. These, usually multidimensional databases must be visualized and mined in order to find interesting objects or to extract meaningful and…
Training a state-of-the-art deep neural network (DNN) is a computationally-expensive and time-consuming process, which incentivizes deep learning developers to debug their DNNs for computational performance. However, effectively performing…
Graph partitioning schedules parallel calculations like sparse matrix-vector multiply (SpMV). We consider contiguous partitions, where the $m$ rows (or columns) of a sparse matrix with $N$ nonzeros are split into $K$ parts without…
Given $n$ points in $\ell_p^d$, we consider the problem of partitioning points into $k$ clusters with associated centers. The cost of a clustering is the sum of $p^{\text{th}}$ powers of distances of points to their cluster centers. For $p…
A $k$-nearest neighbor ($k$NN) query determines the $k$ nearest points, using distance metrics, from a specific location. An all $k$-nearest neighbor (A$k$NN) query constitutes a variation of a $k$NN query and retrieves the $k$ nearest…