Abstract
We consider a generalization of the Rectilinear Steiner Tree problem, where our input is classes of required points instead of simple required points. Our task is to find a minimum rectilinear tree connecting at least one point from each class. We prove that the version, where all required points lie on two parallel lines, called Rectilinear Class Steiner Tree (channel) problem, is NP-hard. But we give a linear time algorithm for the case where the points of each required class are clustered, and the classes consist of non overlapping intervals of points.
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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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Ihler, E. The rectilinear class Steiner tree problem for intervals on two parallel lines. Mathematical Programming 63, 281–296 (1994). https://doi.org/10.1007/BF01582073
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DOI: https://doi.org/10.1007/BF01582073