TY - GEN

T1 - Near-linear approximation algorithms for geometric hitting sets

AU - Agarwal, Pankaj K.

AU - Ezra, Esther

AU - Sharir, Micha

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Cuttings

KW - Geometric range spaces

KW - Hitting sets

UR - http://www.scopus.com/inward/record.url?scp=70849112431&partnerID=8YFLogxK

U2 - 10.1145/1542362.1542368

DO - 10.1145/1542362.1542368

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:70849112431

SN - 9781605585017

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 23

EP - 32

BT - Proceedings of the 25th Annual Symposium on Computational Geometry, SCG'09

T2 - 25th Annual Symposium on Computational Geometry, SCG'09

Y2 - 8 June 2009 through 10 June 2009

ER -