Preprocessing Speed-Up Techniques Is Hard

During the last years, preprocessing-based techniques have been developed to compute shortest paths between two given points in a road network. These speed-up techniques make the computation a matter of microseconds even on huge networks. While there is a vast amount of experimental work in the eld, there is still large demand on theoretical foundations. The preprocessing phases of most speed-up techniques leave open some degree of freedom which, in practice, is lled in a heuristical fashion. Thus, for a given speed-up technique, the problem arises of how to ll the according degree of freedom optimally. Until now, the complexity status of these problems was unknown. In this work, we answer this question by showing NP-hardness for the recent techniques. Part of this report has been published in [3]. However, this work includes all proofs omitted there.