Near-linear approximation algorithms for geometric hitting sets

Pankaj K. Agarwal, Esther Ezra, Micha Sharir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

Given a set system (X,R), the hitting set problem is to find a smallest-cardinality subset H ⊆ X, with the property that each range R ∈ R has a non-empty intersection with H. We present near-linear time approximation algorithms for the hitting set problem, under the following geometric settings: (i) R is a set of planar regions with small union complexity. (ii) R is a set of axis-parallel d-rectangles in ℝd. In both cases X is either the entire d-dimensional space or a finite set of points in d-space. The approximation factors yielded by the algorithm are small; they are either the same as or within an O(log n) factor of the best factors known to be computable in polynomial time.

Original languageEnglish
Title of host publicationProceedings of the 25th Annual Symposium on Computational Geometry, SCG'09
Pages23-32
Number of pages10
DOIs
StatePublished - 2009
Externally publishedYes
Event25th Annual Symposium on Computational Geometry, SCG'09 - Aarhus, Denmark
Duration: 8 Jun 200910 Jun 2009

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Conference

Conference25th Annual Symposium on Computational Geometry, SCG'09
Country/TerritoryDenmark
CityAarhus
Period8/06/0910/06/09

Keywords

  • Approximation algorithms
  • Cuttings
  • Geometric range spaces
  • Hitting sets

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