Automatically calculating periodic time tables in public railway transport
systems is an NP-complete problem with the so called Periodic Event Scheduling
Problem (PESP) [1]. Several optimization tasks based on PESP have to be solved
within the timetabling process. For example, these are finding local conflicts
(small infeasible subnetworks), resolving local conflicts as well as minimizing
weighted slacks for connections [2,3,4]. The given instances represent public railway
transport networks combining the long-distance train paths of Germany with the
most important regional train paths and subnetworks of south, south-west and
south-east Germany.

Corresponding literature:
[1] P. Serafini and W. Ukovich. "A Mathematical Model for Periodic Scheduling
Problems". In: SIAM J. Discrete Math. 2.4 (1989), pp. 550–581.
[2] K. Nachtigall. "Periodic Network Optimization and Fixed Interval Timetable".
Habilitation thesis. University Hildesheim, 1998.
[3] P. Großmann. "On Extracting Minimally Infeasible Periodic Event Net-
works". In: 26th European Conference On Operational Research. Rome,
Italy, 2013.
[4] P. Großmann, S. H ̈olldobler, N. Manthey, K. Nachtigall, J. Opitz, and P.
Steinke. "Solving Periodic Event Scheduling Problems with SAT". In: IEA/AIE.
Vol. 7345. LNAI. Springer, 2012, pp. 166–175.