Treffer: A POLYNOMIAL-TIME APPROXIMATION ALGORITHM FOR A GEOMETRIC DISPERSION PROBLEM.

We consider the following packing problem. Let α be a fixed real in (0, 1]. We are given a bounding rectangle ρ and a set $\cal R$ of n possibly intersecting unit disks whose centers lie in ρ. The task is to pack a set $\cal B$ of m disjoint disks of radius α into ρ such that no disk in B intersects a disk in $\cal R$, where m is the maximum number of unit disks that can be packed. In this paper we present a polynomial-time algorithm for α = 2/3. So far only the case of packing squares has been considered. For that case, Baur and Fekete have given a polynomial-time algorithm for α = 2/3 and have shown that the problem cannot be solved in polynomial time for any α > 13/14 unless ${\cal P}={\cal NP}$. [ABSTRACT FROM AUTHOR]

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