In this section we generalize the routing algorithm of
Section 4 by removing the distinction between
nodes that are terminals and nodes that are not. The algorithm in
this section requires 
word steps, not bit steps. Recall
that in the word model, each edge can transmit a word of 
bits in a single step. The goal of the algorithm is to establish a
set of disjoint paths, each of which may start or end at any node in
the network. The following similar problem was studied by Peleg and
Upfal [27].
Given an expander graph, G, K source nodes,Peleg and Upfal presented polylogarithmic time algorithms for finding K edge-disjoint paths in any n-node expander graph, provided thatin G, and K sink nodes,
in G, where the sources and sinks are all distinct (i.e.,
and
for
, and
for all i and j), construct a path in G from each source
to the corresponding sink
, so that no two paths share an edge.
, where 
is a fixed constant less one. In this
section we show that if we are allowed to specify the network (but not
the locations of the sources and sinks) then it is possible to
construct even more paths. In particular, we describe an n-node
bounded-degree network, R, and show how to find K edge-disjoint
paths in it in 
time, provided that 
.
Furthermore, we show how to find node-disjoint paths between
of the sources and sinks.