Two-dimensional range successor in optimal time and almost linear space

被引：4

作者：

Zhou, Gelin ^{[1
]}

机构：

[1] Univ Waterloo, David R Cheriton Sch Comp Sci, Waterloo, ON N2L 3G1, Canada

来源：

INFORMATION PROCESSING LETTERS | 2016年 / 116卷 / 02期

关键词：

Data structures; Computational geometry; Range successor; Sorted range reporting; Planar orthogonal skyline reporting; QUERIES;

D O I：

10.1016/j.ipl.2015.09.002

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this article, we revisit the problem of supporting two-dimensional range successor queries. We present a data structure with O (n lglg n) words of space and O(lglgn) query time. This improves the work of Nekrich and Navarro (2012) by a factor of lg lgn in query time, or a factor of lg(is an element of) in space cost, where E is an arbitrary positive constant. Our data structure matches the state of the art for two-dimensional range emptiness queries and achieves the optimal query time. This structure has fruitful applications in computational geometry and text indexing. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：171 / 174

页数：4

共 50 条

[1] Two-dimensional peak filter in almost linear time
Belov, A. M.
Verichev, A. V.
Myasnikov, V. V.
[J]. 3RD INTERNATIONAL CONFERENCE INFORMATION TECHNOLOGY AND NANOTECHNOLOGY (ITNT-2017), 2017, 201 : 408 - 416
[2] Linear and nonlinear representations of galilei groups in two-dimensional space-time
Fushchich V.I.
Lagno V.I.
[J]. Ukrainian Mathematical Journal, 1998, 50 (3) : 470 - 480
[3] Optimal Two-Dimensional Lattices for Precoding of Linear Channels
Kapetanovic, Dzevdan
Cheng, Hei Victor
Mow, Wai Ho
Rusek, Fredrik
[J]. IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, 2013, 12 (05) : 2104 - 2113
[4] Two-dimensional continuous wavelet transform as linear phase space representation of two-dimensional signals
Murenzi, R
Antoine, JP
[J]. WAVELET APPLICATIONS IV, 1997, 3078 : 206 - 217
[5] Searchable Symmetric Encryption: Optimal Locality in Linear Space via Two-Dimensional Balanced Allocations
Asharov, Gilad
Naor, Moni
Segev, Gil
Shahaf, Ido
[J]. STOC'16: PROCEEDINGS OF THE 48TH ANNUAL ACM SIGACT SYMPOSIUM ON THEORY OF COMPUTING, 2016, : 1101 - 1114
[6] SEARCHABLE SYMMETRIC ENCRYPTION: OPTIMAL LOCALITY IN LINEAR SPACE VIA TWO-DIMENSIONAL BALANCED ALLOCATIONS
Asharov, Gilad
Naor, Moni
Segev, Gil
Shahaf, Ido
[J]. SIAM JOURNAL ON COMPUTING, 2021, 50 (05) : 1501 - 1536
[7] Linear predictive spectrum estimation algorithm based on space-time two-dimensional
Zhang, Ze
Chen, Hui
Wang, Yongliang
[J]. Xi Tong Gong Cheng Yu Dian Zi Ji Shu/Systems Engineering and Electronics, 2019, 41 (09): : 1937 - 1944
[8] Orthogonal range searching in linear and almost-linear space
Nekrich, Yakov
[J]. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2009, 42 (04): : 342 - 351
[9] Orthogonal range searching in linear and almost-linear space
Nekrich, Yakov
[J]. ALGORITHMS AND DATA STRUCTURES, PROCEEDINGS, 2007, 4619 : 15 - 26
[10] Tight Space Bounds for Two-Dimensional Approximate Range Counting
Wei, Zhewei
Yi, Ke
[J]. ACM TRANSACTIONS ON ALGORITHMS, 2018, 14 (02)

← 1 2 3 4 5 →