Abstract: A fundamental approach in finding efficiently best routes or optimal itineraries in traffic information
systems is to reduce the search space (part of graph visited) of the most commonly used
shortest path routine (Dijkstra˘s algorithm) on a suitably defined graph. We investigate reduction
of the search space while simultaneously retaining data structures, created during a preprocessing
phase, of size linear (i.e., optimal) to the size of the graph. We show that the search space of
Dijkstra˘s algorithm can be significantly reduced by extracting geometric information from a given
layout of the graph and by encapsulating precomputed shortest-path information in resulted geometric
objects (containers). We present an extensive experimental study comparing the impact of
different types of geometric containers using test data from real-world traffic networks. We also
present new algorithms as well as an empirical study for the dynamic case of this problem, where
edge weights are subject to change and the geometric containers have to be updated and show that
our new methods are two to three times faster than recomputing everything from scratch. Finally,
in an appendix, we discuss the software framework that we developed to realize the implementations
of all of our variants of Dijkstra˘s algorithm. Such a framework is not trivial to achieve as our
goal was to maintain a common code base that is, at the same time, small, efficient, and flexible,
as we wanted to enhance and combine several variants in any possible way.
