Optimal point location in a monotone subdivision
SIAM Journal on Computing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Partitioning arrangements of lines, part II: applications
Discrete & Computational Geometry
Approximation algorithms for hitting objects with straight lines
Discrete Applied Mathematics
Approximation algorithms for geometric median problems
Information Processing Letters
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
The SR-tree: an index structure for high-dimensional nearest neighbor queries
SIGMOD '97 Proceedings of the 1997 ACM SIGMOD international conference on Management of data
Two algorithms for nearest-neighbor search in high dimensions
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Locality-preserving hashing in multidimensional spaces
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
A cost model for nearest neighbor search in high-dimensional data space
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
CURE: an efficient clustering algorithm for large databases
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Automatic subspace clustering of high dimensional data for data mining applications
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
The pyramid-technique: towards breaking the curse of dimensionality
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
A constant-factor approximation algorithm for the k-median problem (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
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
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Approximating the diameter, width, smallest enclosing cylinder, and minimum-width annulus
Proceedings of the sixteenth annual symposium on Computational geometry
Similarity Indexing with the SS-tree
ICDE '96 Proceedings of the Twelfth International Conference on Data Engineering
Algorithms for Polytope Covering and Approximation
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Efficient and Effective Clustering Methods for Spatial Data Mining
VLDB '94 Proceedings of the 20th 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
SPRINT: A Scalable Parallel Classifier for Data Mining
VLDB '96 Proceedings of the 22th International Conference on Very Large Data Bases
Approximation Algorithms for k-Line Center
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Proceedings of the twenty-fourth annual symposium on Computational geometry
Squarepants in a tree: Sum of subtree clustering and hyperbolic pants decomposition
ACM Transactions on Algorithms (TALG)
Column Generation for the Minimum Hyperplanes Clustering Problem
INFORMS Journal on Computing
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We consider the following two instances of the projective clustering problem: Given a set S of n points in Rd and an integer k 0, cover S by k slabs (respectively d-cylinders) so that the maximum width of a slab (respectively the maximum diameter of a d-cylinder) is minimized. Let w* be the smallest value so that S can be covered by k slabs (respectively d-cylinders), each of width (respectively diameter) at most w*. This paper contains three main results: (i) For d = 2, we present a randomized algorithm that computes O(k log k) strips of width at most w* that cover S. Its expected running time is O(nk2log4n) if k2 log k ≤ n; for larger values of k, the expected running time is O(n2/3k8/3log14/3n). (ii) For d = 3, a cover of S by O(k log k) slabs of width at most w* can be computed in expected time O(n3/2k9/4polygon(n)).(iii) We compute a cover of S ⊂ Rd by O(dk log k) d-cylinders of diameter at most 8w* in expected time O(dnk3 log4 n). We also present a few extensions of this result.