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<p><b>Abstract</b>—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.</p>
Rectilinear polygon, shortest rectilinear path, minimum bend path, noncrossing paths, computational geometry, VLSI routing.

D. Lee, C. Yang and C. Wong, "The Smallest Pair of Noncrossing Paths in a Rectilinear Polygon," in IEEE Transactions on Computers, vol. 46, no. , pp. 930-941, 1997.
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