Related papers: Optimal Parallel Algorithms for Convex Hulls in 2D…

Much prior work has been done on designing computational geometry algorithms that handle input degeneracies, data imprecision, and arithmetic round-off errors. We take a new approach, inspired by the noisy sorting literature, and study…

The convex hull is a fundamental geometrical structure for many applications where groups of points must be enclosed or represented by a convex polygon. Although efficient sequential convex hull algorithms exist, and are constantly being…

The Convex Hull algorithm is one of the most important algorithms in computational geometry, with many applications such as in computer graphics, robotics, and data mining. Despite the advances in the new algorithms in this area, it is…

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…

In recent years, applications such as real-time simulations, autonomous systems, and video games increasingly demand the processing of complex geometric models under stringent time constraints. Traditional geometric algorithms, including…

In this paper we implemented the algorithm we developed in [1] called 3DPIFCM in a parallel environment by using CUDA on a GPU. In our previous work we introduced 3DPIFCM which performs segmentation of images in noisy conditions and uses…

In this paper, we describe efficient MapReduce simulations of parallel algorithms specified in the BSP and PRAM models. We also provide some applications of these simulation results to problems in parallel computational geometry for the…

We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex…

We describe a pure divide-and-conquer parallel algorithm for computing 3D convex hulls. We implement that algorithm on GPU hardware, and find a significant speedup over comparable CPU implementations.

Finding a good classifier is a multiobjective optimization problem with different error rates and the costs to be minimized. The receiver operating characteristic is widely used in the machine learning community to analyze the performance…

Prune-and-search is an important paradigm for solving many important geometric problems. We show that the general prune-and-search technique can be implemented where the objects are given in read-only memory. As examples we consider…

All-pairs similarity problem asks to find all vector pairs in a set of vectors the similarities of which surpass a given similarity threshold, and it is a computational kernel in data mining and information retrieval for several tasks. We…

Finding the coordinate-wise maxima and the convex hull of a planar point set are probably the most classic problems in computational geometry. We consider these problems in the self-improving setting. Here, we have $n$ distributions…

It has been a long time, since data mining technologies have made their ways to the field of data management. Classification is one of the most important data mining tasks for label prediction, categorization of objects into groups,…

Creation of collision objects for 3D models is a time-consuming task, requiring modelers to manually place primitives such as bounding boxes, capsules, spheres, and other convex primitives to approximate complex meshes. While there has been…

Recently, motivated by the rapid increase of the data size in various applications, Monemizadeh [APPROX'23] and Driemel, Monemizadeh, Oh, Staals, and Woodruff [SoCG'25] studied geometric problems in the setting where the only access to the…

Computationally efficient and automated generation of convex hulls is desirable for high throughput materials discovery of thermodynamically stable multi-species crystal structures. A convex hull genetic algorithm is proposed that uses…

This paper presents a practical GPU-accelerated convex hull algorithm and a novel Sorting-based Preprocessing Approach (SPA) for planar point sets. The proposed algorithm consists of two stages: (1) two rounds of preprocessing performed on…

We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for…

We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…