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A :20piano movers' '

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J H DavenportAuthors Info & Claims

ACM SIGSAM Bulletin, Volume 20, Issue 1-2

Pages 15 - 17

https://doi.org/10.1145/12917.12919

Published: 01 February 1986 Publication History

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Abstract

As has been pointed out [Schwartz & Sharir, 1983b], various problems of motion planning can be expressed as cylindrical algebraic decompositions [Collins, 1975; Arnon et al., 1984]. The purpose of this note is to discuss a particularly simple such problem, and show what actually happens during the decomposition (as far as we could take it). There is no pretence at originality, except perhaps in the conclusions.

References

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Arnon, D. S., Collins, G. E. &amp; McCallum, S., Cylindrical Algebraic Decomposition. SIAM J. Comp. 13(1984) pp. 865--877, 878--889.

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Collins, G. E., Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition. Second GI Conf. Automata Theory and Formal Languages, Springer lecture Notes in Computer Science 33, 1975, pp. 134--183.

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Collins, G. E. &amp; Akritas, A. G., Polynomial Real Root Isolation Using Descartes' Rule of Signs. Proc. SYMSAC 76 (ACM, New York), pp. 272--275.

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Collins, G. E. &amp; Loos, R. G. K., Real Zeros of Polynomials. Computing Supplementum 4 (ed. B. Buchberger, G. E. Collins &amp; R. G. K. Loos), Springer-Verlag, Wien-New York, 1982, pp. 83--94.

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IBM Corp. LISP/VM Reference Manual, SH20-6477-0, IBM, 1984.

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McCallum, S., An Improved Projection Operation for Cylindrical Algebraic Decomposition. Computer Science Tech. Report 548, University of Wisconsin at Madison, Feb. 1985.

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Schwartz, J. T. &amp; Sharir, M., On the "Piano Movers" Problem. I. The Case of a Two-dimensional Rigid Polygonal Body Moving Amidst Polygonal Barriers. Comm. Pure Appl. Math. 36(1983) pp. 345--398.

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Schwartz, J. T. &amp; Sharir, M., On the "Piano Movers" Problem. II. General Techniques for Computing Topological Properties of Real Algebraic Manifolds. Advances in Applied Maths. 4(1983) pp. 298--351.

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(2018)Unsolved Problems, 1969–1999The American Mathematical Monthly10.1080/00029890.1999.12005148106:10(959-962)Online publication date: 23-Apr-2018
https://doi.org/10.1080/00029890.1999.12005148
Wilson DEngland MBradford RDavenport J(2014)Using the Distribution of Cells by Dimension in a Cylindrical Algebraic Decomposition2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing10.1109/SYNASC.2014.15(53-60)Online publication date: Sep-2014
https://doi.org/10.1109/SYNASC.2014.15
Wilson DBradford RDavenport JEngland M(2014)Cylindrical Algebraic Sub-DecompositionsMathematics in Computer Science10.1007/s11786-014-0191-z8:2(263-288)Online publication date: 13-Jun-2014
https://doi.org/10.1007/s11786-014-0191-z
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A :20piano movers' '

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Published In

ACM SIGSAM Bulletin Volume 20, Issue 1-2

Feb/May 1986

56 pages

ISSN:0163-5824

DOI:10.1145/12917

Editor:
Kamal S Abdali

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Association for Computing Machinery

New York, NY, United States

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Published: 01 February 1986

Published in SIGSAM Volume 20, Issue 1-2

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(2018)Unsolved Problems, 1969–1999The American Mathematical Monthly10.1080/00029890.1999.12005148106:10(959-962)Online publication date: 23-Apr-2018
https://doi.org/10.1080/00029890.1999.12005148
Wilson DEngland MBradford RDavenport J(2014)Using the Distribution of Cells by Dimension in a Cylindrical Algebraic Decomposition2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing10.1109/SYNASC.2014.15(53-60)Online publication date: Sep-2014
https://doi.org/10.1109/SYNASC.2014.15
Wilson DBradford RDavenport JEngland M(2014)Cylindrical Algebraic Sub-DecompositionsMathematics in Computer Science10.1007/s11786-014-0191-z8:2(263-288)Online publication date: 13-Jun-2014
https://doi.org/10.1007/s11786-014-0191-z
Wilson DDavenport JEngland MBradford R(2013)A "Piano Movers" Problem ReformulatedProceedings of the 2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing10.1109/SYNASC.2013.14(53-60)Online publication date: 23-Sep-2013
https://dl.acm.org/doi/10.1109/SYNASC.2013.14
Marchand J(2005)The algorithm by schwartz, sharir and collins on the piano mover's problemGeometry and Robotics10.1007/3-540-51683-2_24(49-66)Online publication date: 31-May-2005
https://doi.org/10.1007/3-540-51683-2_24
Arnborg S(2005)Experiments with a projection operator for algebraic decompositionSymbolic and Algebraic Computation10.1007/3-540-51084-2_16(177-182)Online publication date: 27-May-2005
https://doi.org/10.1007/3-540-51084-2_16
Ishiwaka YYoshida TYokoi HKakazu Y(2002)Achieving corporative behavior in heterogeneous agents using hierarchic reinforcement learning-an approach to piano mover's problemIEEE International Conference on Systems, Man and Cybernetics10.1109/ICSMC.2002.1173252(6)Online publication date: 2002
https://doi.org/10.1109/ICSMC.2002.1173252
Eriksson GEriksson HEriksson K(1998)Moving a food trolley around a cornerTheoretical Computer Science10.1016/S0304-3975(97)00121-7191:1-2(193-203)Online publication date: Jan-1998
https://doi.org/10.1016/S0304-3975(97)00121-7
Wang D(1995)Reasoning about Geometric Problems using an Elimination MethodAutomated Practical Reasoning10.1007/978-3-7091-6604-8_8(147-185)Online publication date: 1995
https://doi.org/10.1007/978-3-7091-6604-8_8
Arnon D(1988)A bibliography of quantifier elimination for real closed fieldsJournal of Symbolic Computation10.1016/S0747-7171(88)80016-65:1-2(267-274)Online publication date: 1-Feb-1988
https://dl.acm.org/doi/10.1016/S0747-7171%2888%2980016-6

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