AbstractAn important but difficult combinatorial problem, in general, is to find the optimal route for a single vehicle on a given network. This paper defines a problem type, called the General Routing Problem, and gives an algorithm for its solution. The classical Traveling Salesman Problem and the Chinese Postman Problem are shown to be special limiting cases of the General Routing Problem. The algorithm provides a unified approach to both node and arc oriented routing problems, and exploits special properties of most real transportation networks such as sparsity of the associated adjacency matrix, and the tendency for arc symmetry at many nodes. For node oriented routing problems, this approach tends to produce large reduction in effective problem size.