Inner and outer j-radii of convex bodies in finite-dimensional normed spaces
Discrete & Computational Geometry
Computational complexity of inner and outer j-radii of polytopes in finite-dimensional normed spaces
Mathematical Programming: Series A and B
On the complexity of some basic problems in computational convexity: I.: containment problems
Discrete Mathematics - Special issue: trends in discrete mathematics
Approximation algorithms for geometric problems
Approximation algorithms for NP-hard problems
Approximation algorithms for projective clustering
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Sublinear time approximate clustering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Database-friendly random projections
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Approximate Shape Fitting via Linearization
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating 3D Points with Cylindrical Segments
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Search and Classification of High Dimensional Data
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximation Algorithms for k-Line Center
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
High-dimensional shape fitting in linear time
Proceedings of the nineteenth annual symposium on Computational geometry
Shape dimension and intrinsic metric from samples of manifolds with high co-dimension
Proceedings of the nineteenth 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
Subgradient and sampling algorithms for l1 regression
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
Efficient algorithm for approximating maximum inscribed sphere in high dimensional polytope
Proceedings of the twenty-second annual symposium on Computational geometry
A fast k-means implementation using coresets
Proceedings of the twenty-second annual symposium on Computational geometry
Bi-criteria linear-time approximations for generalized k-mean/median/center
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Sampling-based dimension reduction for subspace approximation
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Efficient subspace approximation algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Computational Geometry: Theory and Applications
Proceedings of the twenty-fourth annual symposium on Computational geometry
Summarizing spatial data streams using ClusterHulls
Journal of Experimental Algorithmics (JEA)
Constructing Laplace operator from point clouds in Rd
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Proceedings of the forty-first annual ACM symposium on Theory of computing
Integral estimation from point cloud in d-dimensional space: a geometric view
Proceedings of the twenty-fifth annual symposium on Computational geometry
Foundations and Trends® in Theoretical Computer Science
Approximating gradients for meshes and point clouds via diffusion metric
SGP '09 Proceedings of the Symposium on Geometry Processing
Cylindrical hierarchy for deforming necklaces
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Clustering lines in high-dimensional space: Classification of incomplete data
ACM Transactions on Algorithms (TALG)
Streaming algorithms for extent problems in high dimensions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Bypassing UGC from some optimal geometric inapproximability results
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Algorithms and hardness for subspace approximation
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Column Generation for the Minimum Hyperplanes Clustering Problem
INFORMS Journal on Computing
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(MATH) Let P be a set of n points in $\Red, and for any integer 0 &xie; k &xie; d--1, let $\RDk(P) denote the minimum over all k-flats $\FLAT$ of maxp&egr;P Dist(p,\FLAT). We present an algorithm that computes, for any 0 k-flat that is within a distance of (1 + $egr;) \RDk(P) from each point of P. The running time of the algorithm is dnO(k/&egr;5log(1/&egr;)). The crucial step in obtaining this algorithm is a structural result that says that there is a near-optimal flat that lies in an affine subspace spanned by a small subset of points in P. The size of this "core-set" depends on k and &egr; but is independent of the dimension.This approach also extends to the case where we want to find a k-flat that is close to a prescribed fraction of the entire point set, and to the case where we want to find j flats, each of dimension k, that are close to the point set. No efficient approximation schemes were known for these problems in high-dimensions, when k1 or j1.