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ABSTRACT
<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>
INDEX TERMS
Rectilinear polygon, shortest rectilinear path, minimum bend path, noncrossing paths, computational geometry, VLSI routing.
CITATION

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.
doi:10.1109/12.609280
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