• Publications
  • Influence
Applications of random sampling in computational geometry, II
  • K. Clarkson
  • Mathematics, Computer Science
  • SCG '88
  • 6 January 1988
TLDR
This paper gives asymptotically tight bounds for several new geometric algorithms. Expand
  • 1,079
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Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm
  • K. Clarkson
  • Mathematics, Computer Science
  • SODA '08
  • 20 January 2008
TLDR
The problem of maximizing a concave function <i>f</i>(<i>x</i>) in a simplex <S</i> can be solved approximately by a simple greedy algorithm, and several coreset bounds are generalized or strengthened. Expand
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Optimal core-sets for balls
Given a set of points [email protected]?R^d and value @e>0, an @[email protected]?P has the property that the smallest ball containing S has radius within [email protected] of the radius of theExpand
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Low-Rank Approximation and Regression in Input Sparsity Time
TLDR
We design a new distribution over m × n matrices S so that, for any fixed n × d matrix A of rank r, with probability at least 9/10, ∥SAx∥2 can be computed in O(nnz(A)) time, where nnz(A) is the number of nonzero entries of A. Expand
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Low rank approximation and regression in input sparsity time
TLDR
We design a new distribution over poly(r ε<sup>-1</sup>) x n matrices S so that for any fixed n x d matrix A of rank r, with probability at least 9/10, SAx<sub>2</sub> = (1 pm ε)Ax simultaneously for all x ∈ R.<sup>d</sup>. Expand
  • 258
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Numerical linear algebra in the streaming model
TLDR
We give near-optimal space bounds in the streaming model for linear algebra problems that include estimation of matrix products, linear regression, low-rank approximation, and approximation of matrix rank. Expand
  • 277
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Smaller core-sets for balls
TLDR
We show that any point-set has an ∊-core-set of size [2/∊]. Expand
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New applications of random sampling in computational geometry
  • K. Clarkson
  • Mathematics, Computer Science
  • Discret. Comput. Geom.
  • 1 June 1987
TLDR
This paper gives several new demonstrations of the usefulness of random sampling techniques in computational geometry. Expand
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  • 24
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Approximation algorithms for shortest path motion planning
TLDR
This paper gives approximation algorithms of solving the following motion planning problem: Given a set of polyhedral obstacles and points <italic>t</italic>, find a shortest path that avoids the obstacles. Expand
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Combinatorial complexity bounds for arrangements of curves and spheres
TLDR
We present upper and lower bounds for extremal problems defined for arrangements of lines, circles, spheres, and alike. Expand
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