Computational complexity of inner and outer j-radii of polytopes in finite-dimensional normed spaces
Mathematical Programming: Series A and B
The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Projective clustering in high dimensions using core-sets
Proceedings of the eighteenth annual symposium on Computational geometry
Server scheduling in the Lp norm: a rising tide lifts all boat
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Load balancing in the L/sub p/ norm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
On the Power of Unique 2-Prover 1-Round Games
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Subgradient and sampling algorithms for l1 regression
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Spectral techniques applied to sparse random graphs
Random Structures & Algorithms
On Non-Approximability for Quadratic Programs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Sampling algorithms for l2 regression and applications
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximating the Cut-Norm via Grothendieck's Inequality
SIAM Journal on Computing
Hardness of approximating the Shortest Vector Problem in high ℓp norms
Journal of Computer and System Sciences - Special issue on FOCS 2003
Tensor-based hardness of the shortest vector problem to within almost polynomial factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
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
Approximating the Radii of Point Sets
SIAM Journal on Computing
The UGC hardness threshold of the ℓp Grothendieck problem
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Sampling algorithms and coresets for ℓp regression
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Coresets and sketches for high dimensional subspace approximation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A unified framework for approximating and clustering data
Proceedings of the forty-third annual ACM symposium on Theory of computing
Bypassing UGC from some optimal geometric inapproximability results
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Zero-one rounding of singular vectors
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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The subspace approximation problem Subspace(k, p) asks for a k dimensional linear subspace that fits a given set of m points in Rn optimally. The error for fitting is a generalization of the least squares fit and uses the lp norm of the distances (l2 distances) of the points from the subspace, e.g., p = ∞ means minimizing the l2 distance of the farthest point from the subspace. Previous work on subspace approximation considers either the case of small or constant k and p [27, 11, 14] or the case of p = ∞ [16, 8, 17, 7, 24, 23, 29].