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Journal ArticleDOI

SMI 2012: Full GPU accelerated convex hull computation

01 Aug 2012-Computers & Graphics (Pergamon)-Vol. 36, Iss: 5, pp 498-506
TL;DR: A hybrid algorithm to compute the convex hull of points in three or higher dimensional spaces using a GPU-based interior point filter to cull away many of the points that do not lie on the boundary and a pseudo-hull that is contained inside the conveX hull of the original points is computed.
About: This article is published in Computers & Graphics.The article was published on 2012-08-01. It has received 46 citations till now. The article focuses on the topics: Convex hull & Convex combination.
Citations
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Proceedings ArticleDOI
01 Dec 2017
TL;DR: In this article, a resource-aware placement scheme is proposed to boost the system performance in a heterogeneous cluster of Docker containers, where the heterogeneity lies in the fact that different nodes in the cluster may have various configurations, concerning resource types and availabilities, etc., and the demands generated by services are varied.
Abstract: Virtualization is a promising technology that has facilitated cloud computing to become the next wave of the Internet revolution. Adopted by data centers, millions of applications that are powered by various virtual machines improve the quality of services. Although virtual machines are well-isolated among each other, they suffer from redundant boot volumes and slow provisioning time. To address limitations, containers were born to deploy and run distributed applications without launching entire virtual machines. As a dominant player, Docker is an open-source implementation of container technology. When managing a cluster of Docker containers, the management tool, Swarmkit, does not take the heterogeneities in both physical nodes and virtualized containers into consideration. The heterogeneity lies in the fact that different nodes in the cluster may have various configurations, concerning resource types and availabilities, etc., and the demands generated by services are varied, such as CPU-intensive (e.g. Clustering services) as well as memory-intensive (e.g. Web services). In this paper, we target on investigating the Docker container cluster and developed, DRAPS, a resource-aware placement scheme to boost the system performance in a heterogeneous cluster.

72 citations

Journal ArticleDOI
TL;DR: A new one-class classification ensemble strategy called approximate polytope ensemble is presented and experimental results show that the proposed strategy is significantly better than state of the art one- class classification methods on over 200 datasets.

51 citations

Journal ArticleDOI
TL;DR: A new one-class classification algorithm capable of working in distributed environments is presented, where convex hull is used to build the boundary of the target class defining the one- class problem in each of the distributed nodes.
Abstract: In this paper, a new one-class classification algorithm capable of working in distributed environments is presented. In it, convex hull is used to build the boundary of the target class defining the one-class problem in each of the distributed nodes. Therefore, we will consider several classifiers, each one determined using a given local data partition, and the goal is to obtain a global classification decision. In order to obtain this final decision, two different algebraic combination rules were proposed: 1) sum and 2) majority voting. Experimental results show that this method opens the possibility of tackling practical one-class classification problems in distributed big data scenarios in an efficient and accurate way.

34 citations


Cites background from "SMI 2012: Full GPU accelerated conv..."

  • ...New implementations have been proposed to deal with this problem [27], [28]....

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Journal ArticleDOI
TL;DR: The works demonstrate that the GPU can be used to solve nontrivial computational geometry problems with significant performance benefit and up to an order of magnitude faster than other sequential convex hull implementations running on the CPU for inputs of millions of points.
Abstract: A novel algorithm is presented to compute the convex hull of a point set in ℝ3 using the graphics processing unit (GPU). By exploiting the relationship between the Voronoi diagram and the convex hull, the algorithm derives the approximation of the convex hull from the former. The other extreme vertices of the convex hull are then found by using a two-round checking in the digital and the continuous space successively. The algorithm does not need explicit locking or any other concurrency control mechanism, thus it can maximize the parallelism available on the modern GPU.The implementation using the CUDA programming model on NVIDIA GPUs is exact and efficient. The experiments show that it is up to an order of magnitude faster than other sequential convex hull implementations running on the CPU for inputs of millions of points. The works demonstrate that the GPU can be used to solve nontrivial computational geometry problems with significant performance benefit.

22 citations

Proceedings ArticleDOI
01 Dec 2014
TL;DR: This publication categorizes existing literature and gives guidelines to choose an appropriate definition of extrapolation for a present problem, and presents hull algorithms, from classic approaches to recent advances, to help the reader to solve a problem, which is affected by extrapolation.
Abstract: Any data based method is vulnerable to the problem of extrapolation, nonetheless there exists no unified theory on handling it. The main topic of this publication is to point out the differences in definitions of extrapolation and related methods. There are many different interpretations of extrapolation and a multitude of methods and algorithms, which address the problem of extrapolation detection in different fields of study. We examine popular definitions of extrapolation, compare them to each other and list related literature and methods. It becomes apparent, that the opinions what extrapolation is and how to handle it, differ greatly from each other. We categorize existing literature and give guidelines to choose an appropriate definition of extrapolation for a present problem. We also present hull algorithms, from classic approaches to recent advances. The presented guidelines and categorized literature enables the reader to categorize a present problem, inspect relevant literature and apply suitable methods and algorithms to solve a problem, which is affected by extrapolation.

20 citations


Cites background from "SMI 2012: Full GPU accelerated conv..."

  • ...As computing time becomes a crucial constraint, several authors develop improvements of algorithm performance by parallelization [42], [43] and by focusing on a graphics processing unit (GPU) for interior point identification [44], [45]....

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References
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01 Jan 1985
TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.
Abstract: From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry...The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two."

6,525 citations


"SMI 2012: Full GPU accelerated conv..." refers background in this paper

  • ...Given a set of points in d-dimensional space, the convex hull is the minimal convex set that contains all the points....

    [...]

  • ...In practice, our culling filter can reduce the number of candidate points by two orders of magnitude....

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Journal ArticleDOI
TL;DR: This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm, and provides empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory.
Abstract: The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory. computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serous errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

5,050 citations


"SMI 2012: Full GPU accelerated conv..." refers methods in this paper

  • ...In practice, the GPU-based filtering algorithm can cull up to 85M interior points per second on an NVIDIA GeForce GTX 580 and the hybrid algorithm improves the overall performance of convex hull computation by 10 − 27 times (for static point sets) and 22 − 46 times (for deforming point sets)....

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Book
01 Jan 1978
TL;DR: In this article, the authors present a coherent treatment of computational geometry in the plane, at the graduate textbook level, and point out the way to the solution of the more challenging problems in dimensions higher than two.
Abstract: From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry...The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two."

3,419 citations

Mark J. Harris1
01 Jan 2011
TL;DR: The water needs of this region have changed in recent years from being primarily for agricultural purposes to domestic and industrial uses now, and the needs of these industries have changed as well.
Abstract: .............................................................................................................1 Table of

747 citations

Journal ArticleDOI
TL;DR: The presented algorithms use the “divide and conquer” technique and recursively apply a merge procedure for two nonintersecting convex hulls to ensure optimal time complexity within a multiplicative constant.
Abstract: The convex hulls of sets of n points in two and three dimensions can be determined with O(n log n) operations. The presented algorithms use the “divide and conquer” technique and recursively apply a merge procedure for two nonintersecting convex hulls. Since any convex hull algorithm requires at least O(n log n) operations, the time complexity of the proposed algorithms is optimal within a multiplicative constant.

731 citations


"SMI 2012: Full GPU accelerated conv..." refers background in this paper

  • ...Given a set of points in d-dimensional space, the convex hull is the minimal convex set that contains all the points....

    [...]