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Discrete & Computational Geometry

, Volume 3, Issue 3, pp 197–217 | Cite as

Lower bounds on moving a ladder in two and three dimensions

  • Yan Ke
  • Joseph O'Rourke
Article

Abstract

It is shown that Ω(n2) distinct moves may be necessary to move a line segment (a “ladder”) in the plane from an initial to a final position in the presence of polygonal obstacles of a total ofn vertices, and that Ω(n4) moves may be necessary for the same problem in three dimensions. These two results establish lower bounds on algorithms that solve the motion-planning problems by listing the moves of the ladder. The best upper bounds known areO(n2 logn) in two dimensions, andO(n5 logn) in three dimensions.

Keywords

Vertical Motion Final Position Discrete Comput Geom Simple Move Polygonal Obstacle 
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 New York Inc. 1988

Authors and Affiliations

  • Yan Ke
    • 1
  • Joseph O'Rourke
    • 1
  1. 1.Department of Computer ScienceJohns Hopkins UniversityBaltimoreUSA

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