Disjoint congruence classes and a timetabling application

Authors:
Geir Dahl
Affiliations:
Center of Mathematics for Applications, University of Oslo, P.O. Box 1053 Blindern, NO-0316 Oslo, Norway and Institute of Transport Economics, N-0349 Oslo, Norway
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

We consider a combinatorial problem motivated by a special simplified timetabling problem for subway networks. Mathematically the problem is to find (pairwise) disjoint congruence classes modulo certain given integers; each such class corresponds to the arrival times of a subway line of a given frequency. For a large class of instances we characterize when such disjoint congruence classes exist and how they may be determined. We also study a generalization involving a minimum distance requirement between congruence classes, and a comparison of different frequency families in terms of their ''efficiency''. Finally, a general method based on integer programming is also discussed.