Abstract
We consider the problem Rectilinear Class Steiner Tree (channel) where we have pairwise not intersecting intervals of required points, partitioned into so called classes, lying on two parallel horizontal lines in the plane. A shortest rectilinear tree is to be found, connecting at least one point of each class. One of our results shows that Rectilinear Class Steiner Tree (channel) is NP-hard, even if each class consists of at most three single points. But we give an exact algorithm that has linear time complexity, if roughly spoken for no vertical line more than a constant number of classes contain points on the right and also not on the right side of this line.
Part of this research was conducted while the author was attending a research initiative at the Leonardo Fibonacci Institute, Povo, Italy.
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© 1993 Springer-Verlag Berlin Heidelberg
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Ihler, E. (1993). Minimum rectilinear steiner trees for intervals on two parallel lines. In: Mayr, E.W. (eds) Graph-Theoretic Concepts in Computer Science. WG 1992. Lecture Notes in Computer Science, vol 657. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56402-0_42
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DOI: https://doi.org/10.1007/3-540-56402-0_42
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