Generalized optimum path search

The author gives a classification of the monotone path functions of a graph. It is shown that one possibility of performing an optimum path search for a generalized path function is to reduce the problem to a shortest path search through the state space. A general algorithm for the optimum path search is proposed and discussed. The proposed algorithm can be considered as a general method of performing a search in the state space for three classes of problems. Modifications of the algorithm for each of the three types of path functions are described. Under some conditions, behavior of the algorithm is close to linear. Finally, an analysis of the implementation of this algorithm for identifying an optimum path in the state space is given