Modeling Costs of Turns in Route Planning

Shortest path algorithms optimize the costs of a journey in a network. For route planning algorithms, networks are usually modeled as graphs. Different cost functions are used, like the length of a path, or the travel time. Costs are traditionally attached to edges in the graph. For some important route planning problems costs that are associated with pairs of edges can be identified. For example, a turn restriction in a traffic network can be represented as a restriction to travel from one edge to another in the graph. A route with minimal turning angles is another example: Costs proportional to the enclosed angles are attached to pairs of adjacent edges. These weights cannot be stored as attributes of nodes or edges in the original graph. We show that these costs can be attached to a linear dual graph. The routing problem can then be solved with the usual algorithms, like Dijkstra’s shortest path algorithm. The linear dual graph solves a problem in modeling turn restrictions: In the original graph, for some shortest paths, nodes may be visited more than once, which is not supported by the usual algorithms. In the linear dual graph, this problem does no longer exist. We also discuss other applications of modeling the turning costs1.