Near-Linear Algorithms for Geometric Hitting Sets and Set Covers

Given a finite range space Σ = ( X , R ) , with N = | X | + | R | , we present two simple algorithms, based on the multiplicative-weight method, for computing a small-size hitting set or set cover of Σ . The first algorithm is a simpler variant of the Brönnimann–Goodrich algorithm but more efficient...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Discrete & computational geometry Ročník 63; číslo 2; s. 460 - 482
Hlavní autori: Agarwal, Pankaj K., Pan, Jiangwei
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.03.2020
Springer Nature B.V
Predmet:
Algorithms
Combinatorics
Computation
Computational Mathematics and Numerical Analysis
Data structures
Disks
Mathematics
Mathematics and Statistics
Zero sum games
Rectangles
Multiplicative weight method
Disks
Geometric set cover
Near-linear algorithms
68U05
52C17
ISSN:0179-5376, 1432-0444
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:Given a finite range space Σ = ( X , R ) , with N = | X | + | R | , we present two simple algorithms, based on the multiplicative-weight method, for computing a small-size hitting set or set cover of Σ . The first algorithm is a simpler variant of the Brönnimann–Goodrich algorithm but more efficient to implement, and the second algorithm can be viewed as solving a two-player zero-sum game. These algorithms, in conjunction with some standard geometric data structures, lead to near-linear algorithms for computing a small-size hitting set or set cover for a number of geometric range spaces. For example, they lead to O ( N polylog ( N ) ) expected-time randomized O (1)-approximation algorithms for both hitting set and set cover if X is a set of points and R a set of disks in R 2 .
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-019-00099-6