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On the 2-Dimensional Channel Assignment Problem
January 1984 (vol. 33 no. 1)
pp. 2-6
D. T. Lee, Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60201.
Joseph Y-T. Leung, Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60201.
We consider the 2-dimensional channel assignment problem: given a set S of iso-oriented rectangles (whose sides are parallel to the coordinate axes), find a minimum number of planes (channels) to which only nonoverlapping rectangles are assigned. This problem is equivalent to the coloring problem of the rectangle intersection graph G = (V, E), in which each vertex in V corresponds to a rectangle and two vertices are adjacent iff their corresponding rectangles overlap, and we ask for an assignment of a minimum number of colors to the vertices such that no adjacent vertices are assigned the same color. We show that the problem is NP-hard.
Citation:
D. T. Lee, Joseph Y-T. Leung, "On the 2-Dimensional Channel Assignment Problem," IEEE Transactions on Computers, vol. 33, no. 1, pp. 2-6, Jan. 1984, doi:10.1109/TC.1984.5009310
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