Related papers: Streaming Algorithms for Planar Convex Hulls
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…
Convex hulls are a fundamental geometric tool used in a number of algorithms. A famous paper by Akl and Toussaint in 1978 described a way to reduce the number of points involved in the computation, which is since known as the Akl-Toussaint…
In the recent years, the scale of graph datasets has increased to such a degree that a single machine is not capable of efficiently processing large graphs. Thereby, efficient graph partitioning is necessary for those large graph…
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 study high-dimensional robust statistics tasks in the streaming model. A recent line of work obtained computationally efficient algorithms for a range of high-dimensional robust estimation tasks. Unfortunately, all previous algorithms…
Estimating the number of subgraphs in data streams is a fundamental problem that has received great attention in the past decade. In this paper, we give improved streaming algorithms for approximately counting the number of occurrences of…
Data streaming, in which a large dataset is received as a "stream" of updates, is an important model in the study of space-bounded computation. Starting with the work of Le Gall [SPAA `06], it has been known that quantum streaming…
We consider the problem of monotone, submodular maximization over a ground set of size $n$ subject to cardinality constraint $k$. For this problem, we introduce the first deterministic algorithms with linear time complexity; these…
The convex hull of a data set $P$ is the smallest convex set that contains $P$. In this work, we present a new data structure for convex hull, that allows for efficient dynamic updates. In a dynamic convex hull implementation, the following…
In this paper, we focus on lower bounds and algorithms for some basic geometric problems in the one-pass (insertion only) streaming model. The problems considered are grouped into three categories: (i) Klee's measure (ii) Convex body…
Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as $k$-center, $k$-median, and $k$-means. Such algorithms…
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…
Problems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases,…
Many existing algorithms for streaming geometric data analysis have been plagued by exponential dependencies in the space complexity, which are undesirable for processing high-dimensional data sets. In particular, once $d\geq\log n$, there…
Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…
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…
We introduce a novel algorithm to perform graph clustering in the edge streaming setting. In this model, the graph is presented as a sequence of edges that can be processed strictly once. Our streaming algorithm has an extremely low memory…
We analyze the correctness of an O(n log n) time divide-and-conquer algorithm for the convex hull problem when each input point is a location determined by a normal distribution. We show that the algorithm finds the convex hull of such…
This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…
A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated…