Related papers: Skyline Diagram: Efficient Space Partitioning for …

Given a simple polygon P in the plane, we present new algorithms and data structures for computing the weak visibility polygon from any query line segment in P. We build a data structure in O(n) time and O(n) space that can compute the…

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…

This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…

Although spatial indexes shorten the query response time, they rely on complex tree structures to narrow down the search space. Such structures in turn yield additional storage overhead and take a toll on index maintenance. Recently, there…

The famous pancake theorem states that for every finite set $X$ in the plane, there exist two orthogonal lines that divide $X$ into four equal parts. We propose an algorithm whose running time is linear in the number of points in $X$ and…

Organizing large-scale resources in a multidimensional semantic space is an approach to efficiently managing and querying resources from different semantic dimensions. To support advanced applications, this paper proposes a resource space…

Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction…

We consider the problem of learning an unknown partition of an $n$ element universe using rank queries. Such queries take as input a subset of the universe and return the number of parts of the partition it intersects. We give a simple…

Horizon or skyline detection plays a vital role towards mountainous visual geo-localization, however most of the recently proposed visual geo-localization approaches rely on \textbf{user-in-the-loop} skyline detection methods. Detecting…

Accurate yet efficient Deep Neural Networks (DNNs) are in high demand, especially for applications that require their execution on constrained edge devices. Finding such DNNs in a reasonable time for new applications requires automated…

Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges…

In this paper I present several novel, efficient, algorithmic techniques for solving some multidimensional geometric data management and analysis problems. The techniques are based on several data structures from computational geometry…

Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…

Path planning algorithms fundamentally aim to compute collision-free paths, with many works focusing on finding the optimal distance path. However, for several applications, a more suitable approach is to balance response time, path safety,…

Voronoi tessellations are used to partition the Euclidean space into polyhedral regions, which are called Voronoi cells. Labeling the Voronoi cells with the class information, we can map any classification problem into a Voronoi…

The basic idea of the kd-tree algorithm is to recursively partition a point set P by hyperplanes, and to store the obtained partitioning in a binary tree. Due to its immense popularity, many applications in astronomy have been implemented.…

Computational methods to compute similarities between floor plans can help architects explore floor plans in large datasets to avoid duplication of designs and to search for existing plans that satisfy their needs. Recently, LayoutGMN…

Given a point set S and an unknown metric d on S, we study the problem of efficiently partitioning S into k clusters while querying few distances between the points. In our model we assume that we have access to one versus all queries that…

An All-to-All Comparison problem is where every element of a data set is compared with every other element. This is analogous to projective planes and affine planes where every pair of points share a common line. For large data sets, the…

k-nearest neighbor (k-NN) search is a fundamental primitive in geometry processing and computer graphics. While spatial partitioning structures such as kd-trees are standard, they are often manifold-blind, failing to exploit the intrinsic…