We study the complexity of the Channel Assignment problem. By applying the
meet-in-the-middle approach we get an algorithm for the ℓ-bounded Channel
Assignment (when the edge weights are bounded by ℓ) running in time
O∗((2ℓ+1)n). This is the first algorithm which breaks the
(O(ℓ))n barrier. We extend this algorithm to the counting variant, at the
cost of slightly higher polynomial factor.
A major open problem asks whether Channel Assignment admits a O(cn)-time
algorithm, for a constant c independent of ℓ. We consider a similar
question for Generalized T-Coloring, a CSP problem that generalizes \CA. We
show that Generalized T-Coloring does not admit a
22o(n)poly(r)-time algorithm, where r is the
size of the instance.Comment: SWAT 2014: 282-29