The authors study the channel pin assignment (CPA) problem subject to position constraints, order constraints, and separation constraints. The problem is to assign two sets of terminals to the top and the bottom of a channel to minimize channel density. It is shown that the problem is NP-hard in general and polynomial time-optimal algorithms are presented for a case where the relative orderings of the terminals on the top and the bottom of the channel are completely fixed. The problem of channel routing with movable modules is introduced, and it is shown that it is a special case of the CPA problem under the formulation, and can be solved optimally in polynomial time. How the algorithms can be incorporated into standard-cell and building-block layout systems is discussed. Experimental results indicate that substantial reduction in channel density can be obtained by allowing movable terminals. >