Moving a ladder in three dimensions: upper and lower bounds

Authors:
Y. Ke;J. O'Rourke
Affiliations:
Department of Computer Science, Johns Hopkins University, Baltimore, MD;Department of Computer Science, Johns Hopkins University, Baltimore, MD
Venue:
SCG '87 Proceedings of the third annual symposium on Computational geometry
Year:
1987

Citing 4
Cited 4

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Abstract

This paper summarizes two results in motion planning, the details of which are in two technical reports. The first establishes an &OHgr;(n4) lower bound on moving a ladder (a line segment) in three dimensions in the presence of polyhedral obstacles with a total of n vertices. This bound is established via a complex arrangement of polygons in space that force a ladder to make &OHgr;(n4 distinct moves between particular initial and final positions. The second report establishes an &Ogr; (n6logn) upper bound by exhibiting an algorithm with that time complexity. The algorithm uses the cell decomposition approach pioneered by Schwartz and Sharir. We suspect that the lower bound is closer to the true complexity of the problem.