On Preprocessing the ALT-Algorithm

In this thesis, we study the preprocessing phase of the ALT algorithm. ALT is a well known preprocessing-based speed-up technique for Dijkstra’s algorithm, which allows fast computations of shortest paths in large scale road networks. The preprocessing of the ALT algorithm has some degree of freedom, in that it must select a subset of nodes in the graph, called landmarks, that fulfill a special role; optimally choosing these landmarks is NP-hard, hence no effective exact solution algorithm exists. In this thesis, we study the landmark selection process; we propose several solution methods, including a greedy algorithm as well as a new heuristic. Furthermore, we propose a new model for the search space of an ALT shortest path computation, which allows us to reduce the problem of optimally choosing k landmarks to the maximum coverage problem, for which approximation results are known, and to formulate the landmark selection problem as an integer linear program.