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Piano Mover's Problem


Given an open subset U in n-dimensional space and two compact subsets C_0 and C_1 of U, where C_1 is derived from C_0 by a continuous motion, is it possible to move C_0 to C_1 while remaining entirely inside U?


See also

Moving Ladder Problem, Moving Sofa Problem

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References

Buchberger, B.; Collins, G. E.; and Kutzler, B. "Algebraic Methods in Geometry." Annual Rev. Comput. Sci. 3, 85-119, 1988.Feinberg, E. B. and Papadimitriou, C. H. "Finding Feasible Points for a Two-point Body." J. Algorithms 10, 109-119, 1989.Finch, S. R. "Moving Sofa Constant." §8.12 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 519-523, 2003.Leven, D. and Sharir, M. "An Efficient and Simple Motion Planning Algorithm for a Ladder Moving in Two-Dimensional Space Amidst Polygonal Barriers." J. Algorithms 8, 192-215, 1987.

Referenced on Wolfram|Alpha

Piano Mover's Problem

Cite this as:

Weisstein, Eric W. "Piano Mover's Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PianoMoversProblem.html

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