Near-linear approximation algorithms for geometric hitting sets

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. Categories and Subject Descriptors F.2.2 [Theory of Computation]: Analysis of Algorithm and Problem Complexity Nonnumerical Algorithms and Problems [Computations on discrete structures, geometrical problems and computations] General Terms Algorithms, Theory. Keywords Geometric range spaces, Hitting se...

• Type: Conference
• Year: 2009
• Where: COMPGEOM
• Authors: Pankaj K. Agarwal, Esther Ezra, Micha Sharir
• Keywords: Approximation Algorithms, COMPGEOM 2009, Discrete Geometry, Hitting Set Problem, Time Approximation Algorithms