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Shortest Path problems are among the most studied network flow optimization problems. Since the end of the 1950's, more than two thousand scientific works have been published in the literature, most of them in journals and conference proceedings concerning general combinatorial optimization on graphs, but also in numerous specialized journals. One of the most interesting application fields is transportation.In many transportation problems, shortest path problems of different kinds need to be solved. These include both classical problems, for example to determine shortest paths (under various measures, such as length, cost and so on) between some given origin/destination pairs in a certain area, and also non standard versions, for example to compute shortest paths either under additional constraints or on particular structured graphs. Due to the nature of the applications, transportation scientists need very flexible and efficient shortest path procedures, both from the running time point of view and in terms of memory requirements. Since no "best" algorithm exists for every kind of transportation problem, Le. no algorithm exists which shows the same practical behavior independently of the structure of the graph, of its size and of the cost measure used for evaluating the paths, research in this field has recently moved to the design and the implementation of "ad hoc" shortest path procedures, which are able to capture the peculiarities of the problems under consideration. Much of the focus has been on the choice and implementation of efficient data structures (see, for instance, Tarjan, 1983). P. Marcotte et al. (eds.), Equilibrium and Advanced Transportation Modelling

A survey of shortest path methods is presented. All the algorithms described are shown to derive from one single prototype method, the difference between them depending only on the particular data structure used in their implementation. This analysis suggests a new classification of the shortest path algorithms. Both the single shortest path tree problem and the all-pairs shortest path problem are considered. One section is dedicated to reoptimization procedures.