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Related papers: Streaming Algorithms for Planar Convex Hulls

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We present a convex hull algorithm that is accelerated on commodity graphics hardware. We analyze and identify the hurdles of writing a recursive divide and conquer algorithm on the GPU and divise a framework for representing this class of…

Computational Geometry · Computer Science 2015-03-20 Stanley Tzeng , John D. Owens

We present data streaming algorithms for the $k$-median problem in high-dimensional dynamic geometric data streams, i.e. streams allowing both insertions and deletions of points from a discrete Euclidean space $\{1, 2, \ldots \Delta\}^d$.…

Data Structures and Algorithms · Computer Science 2017-06-14 Vladimir Braverman , Gereon Frahling , Harry Lang , Christian Sohler , Lin F. Yang

Convex hulls are a fundamental geometric tool used in a number of algorithms. As a side-effect of exhaustive tests for an algorithm for which a convex hull computation was the first step, interesting experimental results were found and are…

Computational Geometry · Computer Science 2013-04-10 Jean Souviron

We study streaming algorithms for Correlation Clustering. Given a graph as an arbitrary-order stream of edges, with each edge labeled as positive or negative, the goal is to partition the vertices into disjoint clusters, such that the…

Data Structures and Algorithms · Computer Science 2025-10-14 Yinhao Dong , Shan Jiang , Shi Li , Pan Peng

Let $P$ be a set of $n$ points in $\mathbb{R}^3$ in general position, and let $RCH(P)$ be the rectilinear convex hull of $P$. In this paper we obtain an optimal $O(n\log n)$-time and $O(n)$-space algorithm to compute $RCH(P)$. We also…

Computational Geometry · Computer Science 2022-09-14 Pablo Pérez-Lantero , Carlos Seara , Jorge Urrutia

As graphs continue to grow in size, we seek ways to effectively process such data at scale. The model of streaming graph processing, in which a compact summary is maintained as each edge insertion/deletion is observed, is an attractive one.…

Data Structures and Algorithms · Computer Science 2014-07-25 Rajesh Chitnis , Graham Cormode , MohammadTaghi Hajiaghayi , Morteza Monemizadeh

Motivated by the desire to cope with data imprecision, we study methods for taking advantage of preliminary information about point sets in order to speed up the computation of certain structures associated with them. In particular, we…

Computational Geometry · Computer Science 2012-12-27 Esther Ezra , Wolfgang Mulzer

The convex hull of a set of points, $C$, serves to expose extremal properties of $C$ and can help identify elements in $C$ of high interest. For many problems, particularly in the presence of noise, the true vertex set (and facets) may be…

Computational Geometry · Computer Science 2016-11-07 Lori Ziegelmeier , Michael Kirby , Chris Peterson

Given a stream of data, a typical approach in streaming algorithms is to design a sophisticated algorithm with small memory that computes a specific statistic over the streaming data. Usually, if one wants to compute a different statistic…

Data Structures and Algorithms · Computer Science 2014-08-13 Vladimir Braverman , Rafail Ostrovsky , Alan Roytman

We present a novel GPU-accelerated implementation of the QuickHull algorihtm for calculating convex hulls of planar point sets. We also describe a practical solution to demonstrate how to efficiently implement a typical Divide-and-Conquer…

Computational Geometry · Computer Science 2018-05-21 Jiayin Zhang , Gang Mei , Nengxiong Xu , Kunyang Zhao

In the adversarially robust streaming model, a stream of elements is presented to an algorithm and is allowed to depend on the output of the algorithm at earlier times during the stream. In the classic insertion-only model of data streams,…

Data Structures and Algorithms · Computer Science 2022-10-24 David P. Woodruff , Samson Zhou

In this paper, we design the first streaming algorithms for the problem of multitasking scheduling on parallel machines with shared processing. In one pass, our streaming approximation schemes can provide an approximate value of the optimal…

Data Structures and Algorithms · Computer Science 2022-04-06 Bin Fu , Yumei Huo , Hairong Zhao

In this paper, we show that if the optimization function is restricted-strongly-convex (RSC) and restricted-smooth (RSM) -- a rich subclass of weakly submodular functions -- then a streaming algorithm with constant factor approximation…

Machine Learning · Computer Science 2018-07-24 Karthik S. Gurumoorthy , Amit Dhurandhar

We consider the problem of estimating the value of max cut in a graph in the streaming model of computation. At one extreme, there is a trivial $2$-approximation for this problem that uses only $O(\log n)$ space, namely, count the number of…

Data Structures and Algorithms · Computer Science 2014-09-09 Michael Kapralov , Sanjeev Khanna , Madhu Sudan

We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less…

Data Structures and Algorithms · Computer Science 2024-12-09 Matthew Ding , Alexandro Garces , Jason Li , Honghao Lin , Jelani Nelson , Vihan Shah , David P. Woodruff

In this article, a new solution for the convex hull problem has been presented. The convex hull is a widely known problem in computational geometry. As nature is a rich source of ideas in the field of algorithms, the solution has been…

Multiagent Systems · Computer Science 2022-12-26 Sina Saadati , Mohammadreza Razzazi

A longstanding observation, which was partially proven in \cite{LNW14,AHLW16}, is that any turnstile streaming algorithm can be implemented as a linear sketch (the reverse is trivially true). We study the relationship between turnstile…

Data Structures and Algorithms · Computer Science 2021-01-06 John Kallaugher , Eric Price

In this paper, we study streaming algorithms that minimize the number of changes made to their internal state (i.e., memory contents). While the design of streaming algorithms typically focuses on minimizing space and update time, these…

Data Structures and Algorithms · Computer Science 2024-06-12 Rajesh Jayaram , David P. Woodruff , Samson Zhou

In the Max-Cut problem in the streaming model, an algorithm is given the edges of an unknown graph $G = (V,E)$ in some fixed order, and its goal is to approximate the size of the largest cut in $G$. Improving upon an earlier result of…

Data Structures and Algorithms · Computer Science 2025-09-08 Yumou Fei , Dor Minzer , Shuo Wang

Applications involving dictionary learning, non-negative matrix factorization, subspace clustering, and parallel factor tensor decomposition tasks motivate well algorithms for per-block-convex and non-smooth optimization problems. By…

Machine Learning · Computer Science 2017-01-27 Konstantinos Slavakis , Georgios B. Giannakis