Constant Factor Approximation for Intersecting Line Segments with Disks
Fast constant factor approximation algorithms are devised for a problem of intersecting a set of n straight line segments with the smallest cardinality set of disks of fixed radii \(r>0\) where the set of segments forms a straight line drawing \(G=(V,E)\) of a planar graph without edge crossings. Exploiting its tough connection with the geometric Hitting Set problem we give \((100+\varepsilon )\)-approximate \(O(n^4\log n)\)-time and \(O(n^2\log n)\)-space algorithm based on the modified Agarwal-Pan reweighting algorithm, where \(\varepsilon >0\) is an arbitrary small constant. Moreover, \(O(n^2\log n)\)-time and \(O(n^2)\)-space 18-approximation is designed for the case where G is any subgraph of a Gabriel graph.
KeywordsComputational geometry Approximation algorithms Hitting set problem Epsilon nets Line segments
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