An approximate algorithm for computing multidimensional convex hulls

被引：7
|
作者：
Xu, ZB
Zhang, JS [1 ]
Leung, YW
机构：
[1] Xian Jiao Tong Univ, Inst Informat & Syst Sci, Res Ctr Appl Math, Xian 710049, Peoples R China
[2] Hong Kong Baptist Univ, Dept Comp Studies, Hong Kong, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 1998年 / 94卷 / 2-3期
关键词：
computational geometry; convex hull; approximate algorithm; simplex and triangulation; best approximation and metric projection;
D O I：
10.1016/S0096-3003(97)10043-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
To find a convex hull for n points in d-dimensional space, the optimal algorithm has time complexity O(n(right) (perpendicular d/2 left perpendicular)). When n and d are large, the execution time is very long. In this paper, we propose an approximate algorithm for computing multidimensional convex hulls. This algorithm finds quasi-two-side approximation to the hull to reduce the time for computing the exact hull boundary. To yield an epsilon-approximate convex hull, it has time complexity O(epsilon(-1/(d-1))n) and storage complexity O(epsilon(-1(d-1))). The approximate algorithm has several advantages: (1) it can easily be implemented, (2) it is suitable for parallel implementation, (3) it is much faster than the exact algorithm, (4) the user can choose to get more accurate results using longer computation time, and (5) it can be applied to solve many problems related to convex hull computation. (C) 1998 Elsevier Science Inc. All rights reserved.
引用
收藏
页码：193 / 226
页数：34
相关论文
共 50 条
  • [21] A complete implementation for computing general dimensional convex hulls
    Emiris, IZ
    INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS, 1998, 8 (02) : 223 - 253
  • [22] Computing simple-path convex hulls in hypergraphs
    Malvestuto, Francesco M.
    Mezzini, Mauro
    Moscarini, Marina
    INFORMATION PROCESSING LETTERS, 2011, 111 (05) : 231 - 234
  • [23] Synergistic Solutions for Merging and Computing Planar Convex Hulls
    Barbay, Jeremy
    Ochoa, Carlos
    COMPUTING AND COMBINATORICS (COCOON 2018), 2018, 10976 : 156 - 167
  • [24] Computing convex hulls and counting integer points with polymake
    Assarf B.
    Gawrilow E.
    Herr K.
    Joswig M.
    Lorenz B.
    Paffenholz A.
    Rehn T.
    Mathematical Programming Computation, 2017, 9 (1) : 1 - 38
  • [25] Approximate Convex Hulls Family for One-Class Classification
    Casale, Pierluigi
    Pujol, Oriol
    Radeva, Petia
    MULTIPLE CLASSIFIER SYSTEMS, 2011, 6713 : 106 - +
  • [26] Output sensitive algorithm for discrete convex hulls
    Comput Geom Theory Appl, 2 (125-138):
  • [27] An output sensitive algorithm for discrete convex hulls
    Har-Peled, S
    COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 1998, 10 (02): : 125 - 138
  • [28] A Fast Training Algorithm for SVM Based on the Convex Hulls Algorithm
    Wu, Chongming
    Wang, Xiaodan
    Bai, Dongying
    Zhang, Hongda
    ICSP: 2008 9TH INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING, VOLS 1-5, PROCEEDINGS, 2008, : 1579 - 1582
  • [29] Convex hulls of spheres and convex hulls of disjoint convex polytopes
    Karavelas, Menelaos I.
    Seidel, Raimund
    Tzanaki, Eleni
    COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2013, 46 (06): : 615 - 630
  • [30] A Practical Solution for Privacy-preserving Approximate Convex Hulls Problem
    Li, Dong
    Huang, Liusheng
    Yang, Wei
    Zhu, Youwen
    Luo, Yonglong
    Li, Lingjun
    Chen, Zhili
    2009 WRI INTERNATIONAL CONFERENCE ON COMMUNICATIONS AND MOBILE COMPUTING: CMC 2009, VOL 3, 2009, : 539 - 544
12345