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Conditions for the Separability of Objects in Two-Dimensional Velocity Fields

Published online by Cambridge University Press:  20 November 2018

Stephan Foldes
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Abstract

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We consider the directed graph representing the obstruction relation between objects moving along the streamlines of a two-dimensional velocity field. A collection of objects is sequentially separable if and only if the corresponding graph has no directed cycles. A sufficient condition for this is the permeability of closed Jordan curves.

Keywords

05C2006A1068R10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 484 - 491
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Birkhoff, G. and Rota, G.-C., Ordinary Differential Equations, John Wiley & Sons, 1969.Google Scholar
2. Duchet, P., Convexity in Combinatorial Structures, Proceedings of the 14th Winter School on Abstract Analysis, Srni, 4-18 Jan. 1986. Suppl. Rend. Circ. Mat. Palermo, Ser. (14) 11(1987), 261–293.Google Scholar
3. Foldes, S., Rival, I. and Urrutia, J., Light Sources, Obstructions and Spherical Orders, Discrete Math.. 102(1992), 13–23.Google Scholar
4. Foldes, S., Sequential Separability of Directionally Convex Objects with Restricted Motion, G-89-21, GERAD and École des Hautes Etudes Commerciales, Montréal, June 1989.Google Scholar
5. Guibas, L.J. and Yao, F.F., On Translating a Set of Rectangles, Proc. 12th Annual ACM Symposium Th. of Comp., (1988), 154-160.Google Scholar
6. Nussbaum, D. and Sack, J.-R., Composite Parts via Translations, Proceedings International Symposium on Optimal Algorithms, Varna, Bulgaria, May 29-June 2, 1989, Lecture Notes in Comput. Sci., Springer- Verlag, 401(153–167).Google Scholar
7. Rival, I. and Urrutia, J., Representing Orders on the Plane by Translating Convex Figures, Order 4(1988), 319–339.Google Scholar
8. Toussaint, G.T., Movable Separability of Sets, in Computational Geometry (G.T. Toussaint, éd.), North Holland, Amsterdam 1985, 335–376.Google Scholar
9. van de Vel, M., Binary Convexities and Distributive Lattices, Proc. London Math. Soc. (3) 48(1984), 1–33.Google Scholar
10. van de Vel, M., Abstract, Topological and Uniform Convex Structures, WS-353, Vrije Universiteit Amsterdam, Faculteit Wiskunde en Informatica, May 1989.Google Scholar