Geographic Decomposition of the Shortest Path Problem, with an Application to the Traffic Assignment Problem

An algorithm, which can be applied to loosely connected networks, is given for geographically decomposing the shortest path problem. The algorithm is applicable to the traffic assignment problem when it is solved as a series of shortest path problems by the Frank-Wolfe algorithm. Numerical results for a large 1287 node, 3752 arc traffic assignment problem for Washington, D.C., indicate that using geographical decomposition can reduce computer memory storage requirements or program run time.