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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Sariel Har-Peled
    • 1
  1. 1.Department of Computer ScienceUniversity of IllinoisUrbanaUSA

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