No, Coreset, No Cry
نویسنده
چکیده
We show that coresets do not exist for the problem of 2-slabs in IR, thus demonstrating that the natural approach for solving approximately this problem efficiently is infeasible. On the positive side, for a point set P in IR, 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.
منابع مشابه
No Coreset, No Cry: II
Let P be a set of n points in d-dimensional Euclidean space, where each of the points has integer coordinates from the range [−∆, ∆], for some ∆ > 1. Let ε > 0 be a given parameter. We show that there is subset Q of P , whose size is polynomial in (log ∆/ε), such that for any k slabs that cover Q, their ε-expansion covers P. In this result, k and d are assumed to be constants. The set Q can als...
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