We provide a general framework for getting linear time constant
factor approximations(and in many cases \FPTAS's) to a copious
amount of well known and well studied problems in Computational
Geometry, such as k-center clustering and furthest nearest
neighbor. The new approach is robust to variations in the input
problem, and yet it is simple, elegant and practical. In particular,
many of these well studied problems which fit easily into our
framework, either previously had no linear time approximation
algorithm, or required rather involved algorithms and analysis.
A short list of the problems we consider include furthest nearest
neighbor, finding the optimal k-center clustering, smallest
disk enclosing k points, k\th largest distance,
k\th smallest m-nearest neighbor distance, k\th
heaviest edge in the \MST and other spanning forest type problems,
problems involving upward closed set systems, and more.
STOC submission: PDF.
Last modified: Wed Oct 31 16:04:28 CDT 2012