Enumerating minimum path decompositions to support route choice set generation

:This paper concerns the structure of movements as were recorded by GPS traces and converted to routes by map matching. Each route in a transportation network corresponds to a collection of directed paths or cycles in a digraph. When considering only directed paths, corresponding to utilitarian trips, the path is not necessarily a shortest path between its origin and destination, and can be split up into a small number of segments, each of which is a shortest or least cost path. Two consecutive segments are separated by split vertices. Split vertices act as intermediate destinations in the mind of travellers who try to hop between them using minimum cost paths. Hence they provide useful information to build route choice models. In this paper we identify and enumerate all possible decompositions of a path into a minimum number of shortest segments. This gives us an indication of the importance of split vertices occurring in particular sets of revealed routes that belong either to a single traveller or to a specific group. The proposed technique allows for automatic extraction of frequently used intermediate destinations (way-points) from revealed preference data.