On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Reconfigurations in graphs and grids
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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Given a pair of start and target configurations, each consisting of n pairwise disjoint disks in the plane, what is the minimum number of moves that suffice for transforming the start configuration into the target configuration? In one move a disk is lifted from the plane and placed back in the plane at another location, without intersecting any other disk. We discuss efficient algorithms for this task and estimate their number of moves under different assumptions on disk radii. We then extend our results for arbitrary disks to systems of pseudodisks, in particular to sets of homothetic copies of a convex object.