We show that coresets do not exist for the problem of 2-slabs
in 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 R^{3},
we describe a near linear time algorithm for computing a
(1+µ)-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.