Z Alternative Routes in Road Networks

We use web-based and autonomous navigation systems in everyday life. These systems produce driving directions by computing a shortest path (or an approximation) with respect to a length function based on various measures, such as distance and travel time. However, optimal paths do not necessarily match the personal preferences of individual users. These preferences may be based on better local knowledge, a bias for or against a certain route segment, or other factors. One can deal with this issue by presenting a small number of alternative paths and hoping one of them will satisfy the user. The goal of an algorithm is to offer alternative paths often, and for these alternatives to look reasonable. Recent research on route planning focused on computing only a single (shortest) path between two given vertices (see [Delling et al. 2009] for an overview). Much less work has been done on finding multiple routes. Some commercial products (by companies such as Google and TomTom) suggest alternative routes using proprietary algorithms. Among published results, a natural approach is to use k-shortest path algorithms [Eppstein 1994], but this is impractical because a reasonable alternative in a road network is probably not among the first few thousand paths. Another approach is to use multi-criteria optimization [Hansen 1979; Martins 1984], in which two or more length functions are optimized at once, and several combinations are returned. Efficient algorithms have been recently presented by Delling and Wagner [2009] and Geisberger et al. [2010]. Our focus is on computing reasonable alternatives with a single length function. In this context, the best published results we are aware of are produced by the choice routing algorithm [Cambridge Vehicle Information Technology Ltd. 2005], which we discuss in Section 4. Although it produces reasonable paths, it is not fully documented and is not fast enough for continental-sized networks.