This paper discusses a new line-routing algorithm. The algorithm has been programmed in FORTRAN II for the IBM 7094 and in FORTRAN IV for the IBM 360/65. It has given good results when applied to many line-routing problems such as mazes, printed circuit boards, substrates, and PERT diagrams. The main advantages of this algorithm, which is based on the continuous plane, over conventional algorithms based on the discrete plane are twofold:   1. Since the algorithm is based on the continuous plane, there is theoretically no limit to the degree of precision used to describe the position of points. In practice, the only factor restricting the precision is the magnitude of the largest (or smallest) number which may be stored in a computer. As a result, the nodes on a printed circuit board, for example, can be input with mil accuracy. If this feat were to be accomplished by existing methods on a 9×9 inch board, a matrix of 81,000,000 cells would have to be stored (and searched) in the computer.   2. The algorithm stores only line segments; therefore to find a path, only the segments that are currently defined need be investigated. Usually with conventional methods, every cell that lies on every possible minimal path must be investigated. The net result is that this algorithm is much faster than the conventional method.
['David W. Hightower']
A solution to line routing problems on the continuous plane