NDLI: Higher-dimensional orthogonal range reporting and rectangle stabbing in the pointer machine model

Please wait, while we are loading the content...

On topological changes in the delaunay triangulation of moving points

The point-set embeddability problem for plane graphs

Protein molecules in 3D: complex behavior from simple local geometry plus weak interactions

Higher-order Erdös: Szekeres theorems

How to walk your dog in the mountains with no magic leash

Approximating low-dimensional coverage problems

Mappings and meshes

Cubic plane graphs on a given point set

Linear-size approximations to the vietoris-rips filtration

Self-improving algorithms for coordinate-wise maxima

Tessellation analysis of the cosmic web

Stabbing horizontal segments with vertical rays

Periodic body-and-bar frameworks

Disjoint edges in complete topological graphs

Configuration space visualization

Geometric packing under non-uniform constraints

Algorithmic complexity of finding cross-cycles in flag complexes

Add isotropic Gaussian kernels at own risk: more and more resilient modes in higher dimensions

Tracing compressed curves in triangulated surfaces

Improved range searching lower bounds

Multinerves and helly numbers of acyclic families

Alexander duality for functions: the persistent behavior of land and water and shore

Finding the maximal empty disk containing a query point

Higher-dimensional orthogonal range reporting and rectangle stabbing in the pointer machine model

On sub-determinants and the diameter of polyhedra

Representing a cubic graph as the intersection graph of axis-parallel boxes in three dimensions

Surface patches from unorganized space curves

Computing cartograms with optimal complexity

Counting crossing-free structures

On the expected complexity of voronoi diagrams on terrains

Testing graph isotopies on surfaces

An output-sensitive algorithm for computing projections of resultant polytopes

Duals of orphan-free anisotropic voronoi diagrams are embedded meshes

Certified computation of planar morse-smale complexes

Conflict-free coloring of points with respect to rectangles and approximation algorithms for discrete independent set

A theorem of bárány revisited and extended

Optimal area-sensitive bounds for polytope approximation

The 2-page crossing number of $K_{n}$

Lang's universal molecule algorithm

Approximate bregman near neighbors in sublinear time: beyond the triangle inequality

A fast and simple surface reconstruction algorithm

On Klee's measure problem for grounded boxes

On laplacians of random complexes

Counting plane graphs: perfect matchings, spanning cycles, and Kasteleyn's technique

Stability of Delaunay-type structures for manifolds: [extended abstract]

A deterministic o(m log m) time algorithm for the reeb graph

Approximating Tverberg points in linear time for any fixed dimension

Improved pointer machine and I/O lower bounds for simplex range reporting and related problems

Object-image correspondence for curves under central and parallel projections

String graphs and incomparability graphs

The sticky geometry of the cosmic web

Higher-dimensional orthogonal range reporting and rectangle stabbing in the pointer machine model

Content Provider	ACM Digital Library
Author	Larsen, Kasper Green Arge, Lars Afshani, Peyman
Abstract	In this paper, we consider two fundamental problems in the pointer machine model of computation, namely orthogonal range reporting and rectangle stabbing. Orthogonal range reporting is the problem of storing a set of n points in d-dimensional space in a data structure, such that the t points in an axis-aligned query rectangle can be reported efficiently. Rectangle stabbing is the "dual" problem where a set of n axis-aligned rectangles should be stored in a data structure, such that the t rectangles that contain a query point can be reported efficiently. Very recently an optimal O(log n+t) query time pointer machine data structure was developed for the three-dimensional version of the orthogonal range reporting problem. However, in four dimensions the best known query bound of $O(log^{2}n$ / log log n + t) has not been improved for decades. We describe an orthogonal range reporting data structure that is the first structure to achieve significantly less than $O(log^{2}n+t)$ query time in four dimensions. More precisely, we develop a structure that uses O(n (log n /log log $n)^{d})$ space and can answer d-dimensional orthogonal range reporting queries (for d ≥ 4) in O( log n (log n /log log $n)^{d-4+1/(d-2)}$ + t) time. Ignoring log log n factors, this speeds up the best previous query time by a $log^{1-1/(d-2)}n$ factor. For the rectangle stabbing problem, we show that any data structure that uses nh space must use Ω(log n (log n / log $h)^{d-2}$ + t) time to answer a query. This improves the previous results by a log h factor, and is the first lower bound that is optimal for a large range of h, namely for h ≥ $log^{d-2+ε}$ n where ε>0 is an arbitrarily small constant. By a simple geometric transformation, our result also implies an improved query lower bound for orthogonal range reporting.
Starting Page	323
Ending Page	332
Page Count	10
File Format	PDF
ISBN	9781450312998
DOI	10.1145/2261250.2261299
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2012-06-17
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Dominance reporting Lower bounds Orthogonal range reporting Pointer machine
Content Type	Text
Resource Type	Article

Central Library (ISO-9001:2015 Certified)
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal, India | PIN - 721302

See location in the Map
03222 282435
Mail: support@ndl.gov.in

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in