Abstract: | We show an O?(n(?+1))-time algorithm for the channel assignment problem, where ? is the maximum edge weight. This improves on the previous O?(n(?+2))-time algorithm by Král (2005) [1], as well as algorithms for important special cases, like L(2,1)-labeling. For the latter problem, our algorithm works in O?(n3) time. The progress is achieved by applying the fast zeta transform in combination with the inclusion-exclusion principle. |