Sliding Disks in the Plane

  • Sergey Bereg
  • Adrian Dumitrescu
  • János Pach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3742)


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 slides in the plane without intersecting any other disk, so that its center moves along an arbitrary (open) continuous curve. We discuss efficient algorithms for this task and estimate their number of moves under different assumptions on disk radii and disk placements. For example, with n congruent disks, \(\frac{3n}{2}+O(\sqrt{n {\rm log}n})\) moves always suffice for transforming the start configuration into the target configuration; on the other hand, \((1+\frac{1}{15}){\it n} - O(\sqrt{n})\) moves are sometimes necessary.


Target Position Small Disk Large Disk Convex Object Black Disk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sergey Bereg
    • 1
  • Adrian Dumitrescu
    • 2
  • János Pach
    • 3
  1. 1.Computer ScienceUniversity of Texas at DallasRichardsonUSA
  2. 2.Computer ScienceUniversity of Wisconsin–MilwaukeeMilwaukeeUSA
  3. 3.Courant Institute of Mathematical SciencesNew YorkUSA

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