Assigning Channels Via the Meet-in-the-Middle Approach

Abstract

We study the complexity of the Channel Assignment problem. By applying the meet-in-the-middle approach we get an algorithm for the (Formula presented.) -bounded Channel Assignment (when the edge weights are bounded by (Formula presented.) ) running in time (Formula presented.). This is the first algorithm which breaks the (Formula presented.) barrier. We extend this algorithm to the counting variant, at the cost of slightly higher polynomial factor. Very recently the second author showed that Channel Assignment does not admit a (Formula presented.) -time algorithm, for a constant c independent of (Formula presented.). We consider a similar question for Generalized (Formula presented.) -Coloring, a CSP problem that generalizes Channel Assignment. We show that Generalized (Formula presented.) -Coloring  does not admit a (Formula presented.) -time algorithm, where r is the size of the instance.