An Algorithm for Path Connections and Its Applications

The algorithm described in this paper is the outcome of an endeavor to answer the following question: Is it possible to find procedures which would enable a computer to solve efficiently path-connection problems inherent in logical drawing, wiring diagramming, and optimal route finding? The results are highly encouraging. Within our framework, we are able to solve the following types of problems: 1) To find a path between two points so that it crosses the least number of existing paths. 2) To find a path between two points so that it avoids as much as possible preset obstacles such as edges. 3) To find a path between two points so that the path is optimal with respect to several properties; for example, a path which is not only one of those which cross the fewest number of existing paths, but, among these, is also one of the shortest. The minimal-distance solution has been programmed on an IBM 704 computer, and a number of illustrations are presented. The class of problems solvable by our algorithm is given in a theorem in Section III. A byproduct of this algorithm is a somewhat remote, but unexpected, relation to physical optics. This is discussed in Section VI.