We introduce the { extsc{Periodic Metro Sched-ul-ing}} ({ extsc{PMS}}) problem,
which aims in generating a
periodic timetable for a given set of routes and a given time
period, in such a way that the minimum time distance between any two
successive trains that pass from the same point of the network is
maximized. This can be particularly useful in cases where trains use
the same rail segment quite often, as happens in metropolitan rail
networks.
We present exact algorithms for ({ extsc{PMS}}) in chain and spider networks,
and constant ratio approximation algorithms for ring networks and
for a special class of tree networks. Some of our algorithms are
based on a reduction to the { extsc{Path Coloring}} problem, while others rely on
techniques specially designed for the new problem
