Abstract
Let A be a plane region which is bounded by an outer rectangle and an inner one and has r rectangular obstacles inside the region. Let k terminal pairs lie on the outer and inner rectangular boundaries. This paper presents an efficient algorithm which finds k “non-crossing” rectilinear paths in the plane region A, each connecting a terminal pair without passing through any obstacles, whose total length is minimum. Non-crossing paths may share common points or line segments but do not cross each other in the plane. The algorithm runs in time O(n log n) where n=r+k.
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J. Takahashi, H. Suzuki, T. Nishizeki, “Algorithms for finding non-crossing paths with minimum total length in plane graphs,” Proc. of ISAAC '92, Lect. Notes in Computer Science, vol. 650, pp. 400–409, 1992.
D. T. Lee, C. F. Shen, C. D. Yang, and C. K. Wong, “Non-crossing path problems,” Manuscript, Dept. of EECS, Northwestern Univ., 1991.
W. Dai, T. Asano and E. S. Kuh, “Routing region definition and ordering scheme for building-block layout,” IEEE Trans. Computer-Aided Design, vol. CAD-4, no. 3, pp. 189–197, July 1985.
P. J. de Rezende, D. T. Lee, Y. F. Wu, “Rectilinear shortest paths in the presence of rectangular barriers,” Discrete & Comput. Geometry, 4, pp. 41–53, 1989.
F. P. Preparata and M. I. Shamos, Computational Geometry, Reading, M.A., Springer-Verlag, 1985.
J. JáJá, An Introduction to Parallel Algorithms, Reading, M.A., Addison Wesley, 1992.
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© 1993 Springer-Verlag Berlin Heidelberg
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Takahashi, Jy., Suzuki, H., Nishizeki, T. (1993). Finding shortest non-crossing rectilinear paths in plane regions. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_239
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DOI: https://doi.org/10.1007/3-540-57568-5_239
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