On-line packing and covering a disk with disks

Open Access
Original Paper


A circular disk D of area |D| can be on-line covered with any sequence of circular disks of total area not smaller than 6.488|D|. Furthermore, any sequence of circular disks whose total area does not exceed 0.197|D| can be on-line packed into D.


On-line covering On-line packing Disk 

Mathematics Subject Classification (2000)

52C15 05B40 


  1. Dumitrescu A., Jiang M.: Covering a disk by disks. Beitr. Algebra Geom. 51(1), 91–109 (2010)MathSciNetMATHGoogle Scholar
  2. Han X., Iwama K., Zhang G.: Online removable square packing. Theory Comput. Syst. 43(1), 38–55 (2008)MathSciNetMATHCrossRefGoogle Scholar
  3. Januszewski J.: On-line covering the unit square with squares. Bull. Pol. Acad. Sci. Math. 57(1), 57–62 (2009)MathSciNetMATHCrossRefGoogle Scholar
  4. Januszewski J., Lassak M.: On-line packing sequences of cubes in the unit cube. Geom. Dedic. 67, 285–293 (1997)MathSciNetMATHCrossRefGoogle Scholar
  5. Kuperberg W.: On-line covering a cube by a sequence of cubes. Discret. Comput. Geom. 12, 83–90 (1994)MathSciNetMATHCrossRefGoogle Scholar
  6. Lassak, M.: A survey of algorithms for on-line packing and covering by sequences of convex bodies, Bolyai Soc. Math. Stud. 6, János Bolyai Math. Soc., Budapest, pp. 129–157 (1997)Google Scholar
  7. Lassak M., Zhang J.: An on-line potato-sack theorem. Discret. Comput. Geom. 6, 1–7 (1991)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Institute of Mathematics and PhysicsUniversity of Technology and Life SciencesBydgoszczPoland

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