Abstract
Given a set D={d1,…,dn} of imprecise points modeled as disks, the minimum diameter problem is to locate a set P={p1,…,pn} of fixed points, where pi∈di, such that the furthest distance between any pair of points in P is as small as possible. This introduces a tight lower bound on the size of the diameter of any instance P. In this paper, we present a fully polynomial time approximation scheme (FPTAS) for computing the minimum diameter of a set of disjoint disks that runs in O(n2ϵ−1) time. Then we relax the disjointness assumption and we show that adjusting the presented FPTAS will cost O(n2ϵ−2) time. We also show that our results can be generalized in Rd when the dimension d is an arbitrary fixed constant.
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