Maintaining the extent of a moving point set

  • Pankaj K. Agarwal
  • Leonidas J. Guibas
  • John Hershberger
  • Eric Veach
Session 2A: Invited Lecture
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1272)


Let S be a set of n moving points in the plane. We give new efficient and compact kinetic data structures for maintaining the diameter, width, and smallest area or perimeter bounding rectangle of the points. When the points in S move with pseudo-algebraic motions, these structures process O(n2+ε) events. We also give constructions showing that μ(n2) combinatorial changes are possible in these extent functions even when the points move on straight lines with constant velocities. We give a similar construction and upper bound for the convex hull, improving known results.


Convex Hull Linear Motion Priority Queue Antipodal Point Flight Plan 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Pankaj K. Agarwal
    • 1
  • Leonidas J. Guibas
    • 2
  • John Hershberger
    • 3
  • Eric Veach
    • 2
  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA
  2. 2.Computer Science DepartmentStanford UniversityStanfordUSA
  3. 3.Mentor Graphics Corp.San JoseUSA

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