A Method for the Solution of the Nth Best Path Problem

A. Definition of a Network. By a network, in this paper, we mean a connected linear graph consisting of points called nodes and directed line segments joining pairs of nodes called links. Associated with each link is a positive real number called the value of the link. Let the variable s with range s = 1, 2, . . , n designate the links in the network; let the variable p with range p = 1, 2, • • • , m designate the nodes of the network. Since the links are directed line segments, each link has an initial node and a terminal node. For a given link s let i (s) designate its initial node and t(s) designate its termina! node; let v(s) denote its value. I t is clear, then, tha t a network is completely specified by a tabulat ion of its links which gives, for each link