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The smallest pair of noncrossing paths in a rectilinear polygon

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1 Author(s)
Yang, C.D. ; Avant! Corp., Sunnyvale, CA

Smallest rectilinear paths are rectilinear paths with simultaneous minimum numbers of bends and minimum lengths. Given two pairs of terminals within a rectilinear polygon, the authors 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, they 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. They 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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Computers, IEEE Transactions on  (Volume:46 ,  Issue: 8 )