Issue No. 01 - January (1984 vol. 33)
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.
D. T. Lee, Joseph Y-T. Leung, "On the 2-Dimensional Channel Assignment Problem", IEEE Transactions on Computers, vol. 33, no. , pp. 2-6, January 1984, doi:10.1109/TC.1984.5009310