Simplex Range Searching and Its Variants: A Review (Q4604367)

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scientific article; zbMATH DE number 6843438

Language	Label	Description	Also known as
English	Simplex Range Searching and Its Variants: A Review	scientific article; zbMATH DE number 6843438

Statements

scholarly article

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Simplex Range Searching and Its Variants: A Review (English)

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A Journey Through Discrete Mathematics

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publication date

26 February 2018

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Pankaj K. Agarwal

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/978-3-319-44479-6_1

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IMPROVED POINTER MACHINE AND I/O LOWER BOUNDS FOR SIMPLEX RANGE REPORTING AND RELATED PROBLEMS

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A general approach for cache-oblivious range reporting and approximate range counting

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Ray Shooting and Parametric Search

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On range searching with semialgebraic sets

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On Range Searching with Semialgebraic Sets. II

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Applications of a new space-partitioning technique

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Ray Shooting Amidst Convex Polygons in 2D

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Ray Shooting Amidst Convex Polyhedra and Polyhedral Terrains in Three Dimensions

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Intersection Queries in Curved Objects

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On Approximating the Depth and Related Problems

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Approximate Halfspace Range Counting

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Approximate range searching

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Approximate polytope membership queries

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Tight lower bounds for halfspace range searching

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Non-partitionable point sets

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Refined bounds on the number of connected components of sign conditions on a variety

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Multidimensional binary search trees used for associative searching

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Multidimensional divide-and-conquer

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How hard is half-space range searching?

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Geometric applications of a randomized optimization technique

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Random Sampling, Halfspace Range Reporting, and Construction of \lowercase$(\le k)$-Levels in Three Dimensions

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Optimal partition trees

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Optimal Deterministic Algorithms for 2-d and 3-d Shallow Cuttings

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Filtering Search: A New Approach to Query-Answering

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A Functional Approach to Data Structures and Its Use in Multidimensional Searching

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Lower bounds for orthogonal range searching: part II. The arithmetic model

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Cutting hyperplanes for divide-and-conquer

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A Spectral Approach to Lower Bounds with Applications to Geometric Searching

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A deterministic view of random sampling and its use in geometry

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Visibility and intersection problems in plane geometry

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The power of geometric duality

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Approximate range searching in higher dimension

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Halfspace range search: An algorithmic application of k-sets

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Simplex range reporting on a pointer machine

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Quasi-optimal upper bounds for simplex range searching and new zone theorems

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Quasi-optimal range searching in spaces of finite VC-dimension

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Algorithms for ray-shooting and intersection searching

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New applications of random sampling in computational geometry

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A Randomized Algorithm for Closest-Point Queries

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Las Vegas algorithms for linear and integer programming when the dimension is small

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Geometric retrieval problems

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Approximate range searching: The absolute model

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Space searching for intersecting objects

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A linear algorithm for determining the separation of convex polyhedra

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Polygonal intersection searching

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A space-optimal solution of general region location

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Halfplanar range search in linear space and \(O(n^{0.695})\) query time

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New lower bounds for Hopcroft's problem

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Space-Time Tradeoffs for Emptiness Queries

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A Lower Bound on the Complexity of Orthogonal Range Queries

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Lower Bounds on the Complexity of Some Optimal Data Structures

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On the Erdős distinct distances problem in the plane

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Relative \((p,\varepsilon )\)-approximations in geometry

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\(\epsilon\)-nets and simplex range queries

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A Pedestrian Approach to Ray Shooting: Shoot a Ray, Take a Walk

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Range minima queries with respect to a random permutation, and approximate range counting

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Linear data structures for fast ray-shooting amidst convex polyhedra

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Sharp bounds for vertical decompositions of linear arrangements in four dimensions

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On Range Searching in the Group Model and Combinatorial Discrepancy

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Improved range searching lower bounds

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Construction of \(\epsilon\)-nets

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Cutting hyperplane arrangements

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Efficient partition trees

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Reporting points in halfspaces

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Linear Optimization Queries

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Range searching with efficient hierarchical cuttings

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Using the Borsuk-Ulam theorem. Lectures on topological methods in combinatorics and geometry. Written in cooperation with Anders Björner and Günter M. Ziegler

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Multilevel polynomial partitions and simplified range searching

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On ray shooting in convex polytopes

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Applying Parallel Computation Algorithms in the Design of Serial Algorithms

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Linear programming queries revisited

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General methods for adding range restrictions to decomposable searching problems

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Semialgebraic Range Reporting and Emptiness Searching with Applications

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Polygon Retrieval

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On the Complexity of Maintaining Partial Sums

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Partitioning Space for Range Queries

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Identifiers

zbMATH Open document ID

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10.1007/978-3-319-44479-6_1

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:4604367

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