Abstract
It is shown that Ω(n 2) 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(n 4) 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(n 2 logn) in two dimensions, andO(n 5 logn) in three dimensions.
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This work was partially supported by NSF Grants DCR-83-51468 and grants from Martin Marietta, IBM, and General Motors.
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Ke, Y., O'Rourke, J. Lower bounds on moving a ladder in two and three dimensions. Discrete Comput Geom 3, 197–217 (1988). https://doi.org/10.1007/BF02187908
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DOI: https://doi.org/10.1007/BF02187908