Given a graph with arcs that have costs, the A* algorithm is designed to find the shortest path from a single node to a set of nodes. While the A* algorithm is well understood, it is somewhat limited in its application due to the fact that it is often difficult to specify the "heuristic function" so that A* exhibits desirable computational properties. In this paper a metric space approach to the specification of the heuristic function is introduced. It is shown how to specify an admissible and monotone heuristic function for a wide class of problem domains. In addition, when the cost structure for the underlying graph is specified via a metric, it is shown that admissible and monotone heuristic functions are easy to specify and further computational advantages can be obtained. Applications to an optimal parts distribution problem in flexible manufacturing systems and artificial intelligence planning problems are provided.< >