In this paper the problem of routing messages along shortest paths in
a distributed network without using complete routing tables is conside
red. In particular, the complexity of deriving minimum (in terms of nu
mber of intervals) interval routing schemes is analyzed under differen
t requirements. For all the cases considered NP-hardness proofs are gi
ven, while some approximability results are provided. Moreover, relati
ons among the different cases considered are studied.