On the 2-Dimensional Channel Assignment Problem

Authors:
D. T. Lee;Joseph Y-T. Leung
Affiliations:
Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60201.;Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60201.
Venue:
IEEE Transactions on Computers
Year:
1984

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Abstract

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.