The problem studied in this paper is the channel routing problem to assign points with p colors on the upper row of the channel to points on the lower row in order to minimize its density. The case that the points on the upper row has an identical color or only two colors is studied in [1, 2]. This paper generalizes that to the points with p colors. First, we consider the problem to determine whether there is an assignment with density less than or equal to d, when an arbitrary d is given. We show that the problem is solved in O(p(n+m)log(n+m)) time. Using this result, we resolve the problem to fine an assignment with a minimum density.