Online search for a hyperplane in high-dimensional Euclidean space

被引：2

作者：

Antoniadis, Antonios ^{[1
]}

Hoeksma, Ruben ^{[1
]}

Kisfaludi-Bak, Sandor ^{[2
]}

Schewior, Kevin ^{[3
]}

机构：

[1] Univ Twente, Dept Appl Math, Enschede, Netherlands

[2] Aalto Univ, Dept Comp Sci, Espoo, Finland

[3] Univ Cologne, Dept Math & Comp Sci, Cologne, Germany

来源：

INFORMATION PROCESSING LETTERS | 2022年 / 177卷

关键词：

Sphere inspection; Online search problem; On-line algorithms; Computational geometry; Cow-path problem;

D O I：

10.1016/j.ipl.2022.106262

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider the online search problem in which a server starting at the origin of a d-dimensional Euclidean space has to find an arbitrary hyperplane. The best-possible competitive ratio and the length of the shortest curve from which each point on the d dimensional unit sphere can be seen are within a constant factor of each other. We show that this length is in 1(d) & AND; O(d(3/2)).(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页数：4

共 50 条

[1] Reporting Neighbors in High-Dimensional Euclidean Space
Aiger, Dror
Kaplan, Haim
Sharir, Micha
[J]. PROCEEDINGS OF THE TWENTY-FOURTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA 2013), 2013, : 784 - 803
[2] REPORTING NEIGHBORS IN HIGH-DIMENSIONAL EUCLIDEAN SPACE
Aiger, Dror
Kaplan, Haim
Sharir, Micha
[J]. SIAM JOURNAL ON COMPUTING, 2014, 43 (04) : 1363 - 1395
[3] Reflection-Like Maps in High-Dimensional Euclidean Space
Huang, Zhiyong
Li, Baokui
[J]. MATHEMATICS, 2020, 8 (06)
[4] Homology of moduli spaces of linkages in high-dimensional Euclidean space
Schuetz, Dirk
[J]. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2013, 13 (02): : 1183 - 1224
[5] An effective method for approximating the Euclidean distance in high-dimensional space
Jeong, Seungdo
Kim, Sang-Wook
Kim, Kidong
Choi, Byung-Uk
[J]. DATABASE AND EXPERT SYSTEMS APPLICATIONS, PROCEEDINGS, 2006, 4080 : 863 - 872
[6] Dimensionality reduction for similarity search with the Euclidean distance in high-dimensional applications
Jeong, Seungdo
Kim, Sang-Wook
Choi, Byung-Uk
[J]. MULTIMEDIA TOOLS AND APPLICATIONS, 2009, 42 (02) : 251 - 271
[7] Dimensionality reduction for similarity search with the Euclidean distance in high-dimensional applications
Seungdo Jeong
Sang-Wook Kim
Byung-Uk Choi
[J]. Multimedia Tools and Applications, 2009, 42 : 251 - 271
[8] Polynomial approximate discretization of geometric centers in high-dimensional Euclidean space
Vladimir Shenmaier
[J]. Advances in Data Analysis and Classification, 2022, 16 : 1039 - 1067
[9] Polynomial approximate discretization of geometric centers in high-dimensional Euclidean space
Shenmaier, Vladimir
[J]. ADVANCES IN DATA ANALYSIS AND CLASSIFICATION, 2022, 16 (04) : 1039 - 1067
[10] Fast nearest neighbor search in high-dimensional space
Berchtold, S
Ertl, B
Keim, DA
Kriegel, HP
Seidl, T
[J]. 14TH INTERNATIONAL CONFERENCE ON DATA ENGINEERING, PROCEEDINGS, 1998, : 209 - 218

← 1 2 3 4 5 →