Optimal backboard ordering through the shortest path algorithm

The problem dealt with in this paper is the optimal ordering of mother boards of a vast digital system, for instance, so that the total length of the interconnecting wires will be minimal. It is shown that a directed and weighted linear graph may be produced, on which this problem is equivalent to the well-known problem of finding the shortest path between a unique source and a unique sink. An algorithm for tracing the shortest path is presented. This algorithm takes advantage of the special features of the auxiliary graph and reduces significantly the computational effort required. Some upper bounds on the number of operations needed are included.