Add to ORKGAbstract We speed up previous (1 + ")-factor approximation algorithms for a number of geometric optimization problems in fixed dimensions: diameter, width, minimum-radius enclosing cylinder, minimum-width enclosing annulus, minimum-width enclosing cylindrical shell, etc. Linear time bounds were known before; we further improve the dependence of the "constants " in terms of ". We next consider the data-stream model and present new (1 + ")-factor approximation algorithms that need only constant space for all of the above problems in any fixed dimension. Previously, such a result was known only for diameter. Both sets of results are obtained using the core-set framework recently proposed by Agarwal,...
In this thesis we show that, for several clustering problems, we can extract a small set of points, ...
In this paper, we show that for several clustering problems one can extract a small set of points, s...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
AbstractWe speed up previous (1+ε)-factor approximation algorithms for a number of geometric optimiz...
We present a new streaming algorithm for maintaining an ε-kernel of a point set in Rd using O((1/ε(d...
We define a class of algorithms for constructing coresets of (geometric) data sets, and show that al...
We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions. Us...
Abstract. We study the problem of maintaining a (1+ɛ)-factor approximation of the diameter of a stre...
<p>Large scale geometric data is ubiquitous. In this dissertation, we design algorithms and data str...
We apply the polynomial method - specifically, Chebyshev polynomials - to obtain a number of new res...
Introduced by Agarwal, Har-Peled, and Varadarajan [J. ACM, 2004], an epsilon-kernel of a point set i...
International audienceThe computation of (i) ε-kernels, (ii) approximate diameter, and (iii) approxi...
In this paper, we show that there exists a small core-set for the problem of computing the “smallest...
The paradigm of coresets has recently emerged as a powerful tool for efficiently approximating vario...
International audienceNumerous approximation algorithms for problems on unit disk graphs have been p...
In this thesis we show that, for several clustering problems, we can extract a small set of points, ...
In this paper, we show that for several clustering problems one can extract a small set of points, s...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
AbstractWe speed up previous (1+ε)-factor approximation algorithms for a number of geometric optimiz...
We present a new streaming algorithm for maintaining an ε-kernel of a point set in Rd using O((1/ε(d...
We define a class of algorithms for constructing coresets of (geometric) data sets, and show that al...
We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions. Us...
Abstract. We study the problem of maintaining a (1+ɛ)-factor approximation of the diameter of a stre...
<p>Large scale geometric data is ubiquitous. In this dissertation, we design algorithms and data str...
We apply the polynomial method - specifically, Chebyshev polynomials - to obtain a number of new res...
Introduced by Agarwal, Har-Peled, and Varadarajan [J. ACM, 2004], an epsilon-kernel of a point set i...
International audienceThe computation of (i) ε-kernels, (ii) approximate diameter, and (iii) approxi...
In this paper, we show that there exists a small core-set for the problem of computing the “smallest...
The paradigm of coresets has recently emerged as a powerful tool for efficiently approximating vario...
International audienceNumerous approximation algorithms for problems on unit disk graphs have been p...
In this thesis we show that, for several clustering problems, we can extract a small set of points, ...
In this paper, we show that for several clustering problems one can extract a small set of points, s...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...