Abstract
We show that coresets do not exist for the problem of 2-slabs in \({\mathbb R}^{3}\), thus demonstrating that the natural approach for solving approximately this problem efficiently is infeasible. On the positive side, for a point set P in \({\mathbb R}^{3}\), we describe a near linear time algorithm for computing a (1+ε)-approximation to the minimum width 2-slab cover of P. This is a first step in providing an efficient approximation algorithm for the problem of covering a point set with k-slabs.
The full version of this paper is available from http://www.uiuc.edu/sariel papers/02/http://www.uiuc.edu/sariel/papers/02/2slab/2slab/.
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Har-Peled, S. (2004). No, Coreset, No Cry. In: Lodaya, K., Mahajan, M. (eds) FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2004. Lecture Notes in Computer Science, vol 3328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30538-5_27
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