Modern fast packet switching networks are being forced to rethink the
routing schemes that are used in more traditional networks. The reexam
ination is necessitated because in these fast networks switches on the
message's route can afford to make only minimal and simple operations
. For example, examining a table of a size proportional to the network
size is out of the question. In this paper we examine routing strateg
ies for such network based on flooding and predefined routes. Our conc
ern is to get both efficient routing and an even (balanced) use of net
work resources. We present efficient algorithms for assigning weights
to edges in a controlled flooding scheme but show that the flooding sc
heme is not likely to yield a balanced use of the resources. We then p
resent efficient algorithms for choosing routes along: 1) bfs trees an
d 2) shortest paths. We show that in both cases a balanced use of netw
ork resources can be guaranteed.