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The Smallest Pair of Noncrossing Paths in a Rectilinear Polygon
August 1997 (vol. 46 no. 8)
pp. 930-941

Abstract—Smallest rectilinear paths are rectilinear paths with a minimum number of bends and with a minimum length simultaneously. In this paper, given two pairs of terminals within a rectilinear polygon, we derive an algorithm to find a pair of noncrossing rectilinear paths within the polygon such that the total number of bends and the total length are both minimized. Although a smallest rectilinear path between two terminals in a rectilinear polygon always exists, we show that such a smallest pair may not exist for some problem instances. In that case, the algorithm presented will find, among all noncrossing paths with a minimum total number of bends, a pair whose total length is the shortest, or find, among all noncrossing paths with a minimum total length, a pair whose total number of bends is minimized. We provide a simple linear time and space algorithm based on the fact that there are only a limited number of configurations of such a solution pair.

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Index Terms:
Rectilinear polygon, shortest rectilinear path, minimum bend path, noncrossing paths, computational geometry, VLSI routing.
Citation:
C.d. Yang, D.t. Lee, C.k. Wong, "The Smallest Pair of Noncrossing Paths in a Rectilinear Polygon," IEEE Transactions on Computers, vol. 46, no. 8, pp. 930-941, Aug. 1997, doi:10.1109/12.609280
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