Permutation layout with arbitrary between-pins capacities

The permutation layout problem is considered under the constraints that no wire pass in the area above the upper line, no wire cross the lower line more than once, and the number of wires passing between two adjacent pins on the lower line not be greater than a given nonnegative number for each such pair. It is shown that a solution can be found in O(n²) time by dynamic programming, where n is the number of nets to be realized