Affiliation:
1. University of Illinois, Urbana-Champaign, Urbana, IL
2. University of Texas at Dallas, Richardson, TX
Abstract
We provide a general framework for getting expected linear time constant factor approximations (and in many cases FPTAS's) to several well known problems in Computational Geometry, such as
k
-center clustering and farthest 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 farthest nearest neighbor,
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. Finally, we show how to extend our framework such that the linear running time bound holds with high probability.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference43 articles.
1. P. K. Agarwal S. Har-Peled and K. Varadarajan. 2005. Geometric approximation via coresets. In Combinatorial and Computational Geometry J. E. Goodman J. Pach and E. Welzl (Eds.). Cambridge New York. P. K. Agarwal S. Har-Peled and K. Varadarajan. 2005. Geometric approximation via coresets. In Combinatorial and Computational Geometry J. E. Goodman J. Pach and E. Welzl (Eds.). Cambridge New York.
2. Approximating extent measures of points
3. Applications of Parametric Searching in Geometric Optimization
4. Achieving anonymity via clustering
5. On Approximating the Depth and Related Problems
Cited by
10 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献