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Representing orders on the plane by translating convex figures

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Abstract

Given a finite collection of disjoint, convex figures on the plane, is it possible to assign to each a single direction of motion so that this collection of figures may be separated, through an arbitrary large distance, by translating each figure one at a time, along its assigned direction? We present a computational model for this separability problem based on the theory of ordered sets.

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References

  • B.Bollobas (1977) Colouring lattices,Alg. Univ. 7, 313–314.

    Google Scholar 

  • B. Chazelle, T. Ottmann, E. Soisalon-Soininen, and D. Wood (1983) The complexity and decidability of separation, Tech. Report CS-83-34, University of Waterloo.

  • R.Dawson (1984) On removing a ball without disturbing the others,Math. Mag. 57, 27–30.

    Google Scholar 

  • P.Erdös (1959) Graph theory and probability,Canad. J. Math. 11, 34–38.

    Google Scholar 

  • I.Fáry (1948) On the straight line representation of planar graphs,Acta. Sci. Math. (Szeged) 11, 229–233.

    Google Scholar 

  • L. J. Guibas and F. F. Yao (1980) On translating a set of rectangles,Proc. 12th Annual ACM Symposium Th. of Comp., pp. 154–160.

  • D.Kelly (1981) On the dimension of partially ordered sets,Discrete Math. 35, 135–156.

    Google Scholar 

  • D. Kelly (1987) Fundamentals of planar ordered sets,Discrete Math.

  • D.Kelly and I.Rival (1975) Planar lattices,Canad. J. Math. 27, 636–665.

    Google Scholar 

  • M. Mansouri and G. T. Toussaint (1985) Translation queries for convex polygons,Proc. IASTED Internat. Sympos. Robotics and Automation., Lugano, Switzerland.

  • J.Nešetřil and V.Rödl (1984) Combinatorial partitions of finite posets and lattices-Ramsey lattices,Alg. Univ. 19, 106–119.

    Google Scholar 

  • R. Nowakowski, I. Rival, and J. Urrutia (1987) Representing orders on the plane by translating points and lines, to appear.

  • J.-R. Sack and G. T. Toussaint (1985) Translating polygons in the plane,Proc. STACS '85, Saarbrücken, pp. 310–321.

  • G. T.Toussaint (1985) Movable separability of sets, inComputational Geometry (G. T.Toussaint, ed.), North Holland, Amsterdam, pp. 335–376.

    Google Scholar 

  • B.Sands (1985) Problem 2.7, inGraphs and Order (ed. I.Rival), D. Reidel, Dordrecht, p. 531.

    Google Scholar 

  • G. X. Viennot (1985) Problèmes combinatoires posés par la physique statistique, Séminaire Bourbaki, No. 626, inAstérisque, No. 121-122 225-246.

  • K.Wagner (1936) Bemerkungen zum Vierfarbenproblem,Jber. Deutsch. Math. Verein. 46, 26–32.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Ottawa, KIN9B4, Ottawa, Canada

    Ivan Rival & Jorge Urrutia

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  1. Ivan Rival
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  2. Jorge Urrutia
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Communicated by P. Hell

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Rival, I., Urrutia, J. Representing orders on the plane by translating convex figures. Order 4, 319–339 (1988). https://doi.org/10.1007/BF00714475

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  • DOI: https://doi.org/10.1007/BF00714475

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