Approximation Algorithms for k-Line Center

Authors:
Pankaj K. Agarwal;Cecilia Magdalena Procopiuc;Kasturi R. Varadarajan
Affiliations:
-;-;-
Venue:
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Year:
2002

Citing 19
Cited 16

Computing the Width of a Set

IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximation algorithms for hitting objects with straight lines

Discrete Applied Mathematics
Las Vegas algorithms for linear and integer programming when the dimension is small

Journal of the ACM (JACM)
FastMap: a fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasets

SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Locality-preserving hashing in multidimensional spaces

STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Efficient algorithms for geometric optimization

ACM Computing Surveys (CSUR)
Fast algorithms for projected clustering

SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Efficient approximation and optimization algorithms for computational metrology

SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Efficiently approximating the minimum-volume bounding box of a point set in three dimensions

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Data clustering: a review

ACM Computing Surveys (CSUR)
Finding generalized projected clusters in high dimensional spaces

SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
Approximating the diameter, width, smallest enclosing cylinder, and minimum-width annulus

Proceedings of the sixteenth annual symposium on Computational geometry
Approximation algorithms for projective clustering

SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Projective clustering in high dimensions using core-sets

Proceedings of the eighteenth annual symposium on Computational geometry
A Monte Carlo algorithm for fast projective clustering

Proceedings of the 2002 ACM SIGMOD international conference on Management of data
Optimal Grid-Clustering: Towards Breaking the Curse of Dimensionality in High-Dimensional Clustering

VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
Local Dimensionality Reduction: A New Approach to Indexing High Dimensional Spaces

VLDB '00 Proceedings of the 26th International Conference on Very Large Data Bases
The Two-Line Center Problem from a Polar View: A New Algorithm and Data Structure

WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Approximate Shape Fitting via Linearization

FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science

Curve reconstruction from noisy samples

Proceedings of the nineteenth annual symposium on Computational geometry
Approximation algorithms for projective clustering

Journal of Algorithms
A (1 + ɛ)-approximation algorithm for 2-line-center

Computational Geometry: Theory and Applications
Practical methods for shape fitting and kinetic data structures using core sets

SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On coresets for k-means and k-median clustering

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximating extent measures of points

Journal of the ACM (JACM)
A simple linear algorithm for computing rectilinear 3-centers

Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
Analysis of incomplete data and an intrinsic-dimension Helly theorem

SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Matrix approximation and projective clustering via volume sampling

SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Bi-criteria linear-time approximations for generalized k-mean/median/center

SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Private coresets

Proceedings of the forty-first annual ACM symposium on Theory of computing
A near-linear algorithm for projective clustering integer points

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Data reduction for weighted and outlier-resistant clustering

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
No coreset, no cry: II

FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
No, coreset, no cry

FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
An effective coreset compression algorithm for large scale sensor networks

Proceedings of the 11th international conference on Information Processing in Sensor Networks

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given a set P of n points in Rd and an integer k 驴 1, let w* denote the minimum value so that P can be covered by k cylinders of radius at most w*. We describe an algorithm that, given P and an 驴 0, computes k cylinders of radius at most (1 + 驴)w* that cover P. The running time of the algorithm is O(n log n), with the constant of proportionality depending on k, d, and 驴. We first show that there exists a small "certificate" Q 驴 P, whose size does not depend on n, such that for any k-cylinders that cover Q, an expansion of these cylinders by a factor of (1 + 驴) covers P. We then use a well-known scheme based on sampling and iterated re-weighting for computing the cylinders.