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On Bends and Distances of Paths Among Obstacles in Two-Layer Interconnection Model
June 1994 (vol. 43 no. 6)
pp. 711-724

We consider problems of finding assorted rectilinear paths among rectilinear obstacles in a two-layer interconnection model according to the number of bends and the 1-layer distance (y-distance). Using a horizontal wave-front approach, optimal /spl theta/(e log e) time algorithms are presented to find the shortest path and the minimum-bend path using linear space, and to find the shortest minimum-bend path and the minimum-bend shortest path using O(e log e) space, where e is the number of obstacle edges. By the same approach, we also derive an algorithm for finding a shortest two-layer distance (xy-distance) minimum-bend path in optimal /spl theta/(e log e) time using O(e log e) space.

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Index Terms:
multiprocessor interconnection networks; computational geometry; computational complexity; network synthesis; minimisation of switching nets; bends; distances; paths; obstacles; two-layer interconnection model; rectilinear paths; horizontal wave-front approach; optimal time algorithms; shortest path; minimum-bend path; linear space; VLSI; 2-terminal wire routing; computational geometry.
D.T. Lee, C.D. Yang, C.K. Wong, "On Bends and Distances of Paths Among Obstacles in Two-Layer Interconnection Model," IEEE Transactions on Computers, vol. 43, no. 6, pp. 711-724, June 1994, doi:10.1109/12.286304
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