On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
The densest packing of equal circles into a parallel strip
Discrete & Computational Geometry
New results in the packing of equal circles in a square
Discrete Mathematics
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
A Survey on Obnoxious Facility Location Problems
A Survey on Obnoxious Facility Location Problems
Shortest path amidst disc obstacles is computable
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
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We consider the problem of placing a maximal number of disks in a rectangular region containing obstacles such that no two disks intersect. Let α be a fixed real in (0,1]. We are given a bounding rectangle P and a set $\cal{R}$ of possibly intersecting unit disks whose centers lie in P. The task is to pack a set $\cal{B}$ of m disjoint disks of radius α into P such that no disk in $\cal{B}$ intersects a disk in $\cal{R}$, where m is the maximum number of unit disks that can be packed. Baur and Fekete showed that the problem cannot be solved in polynomial time for α≥13/14, unless ${\cal P}={\cal NP}$. In this paper we present an algorithm for α= 2/3.