The main result of this section is summarized in the following theorem.
Proof:
There are three phases to the algorithm. First,
packets originating at bad nodes are deterministically routed to the
good nodes with which they are associated. By
Lemma 5.4 this phase requires 
steps. Next,
packets are routed between the good nodes on the logical network.
Since at most 
bad nodes are associated with each good
necklace, with high probability the congestion of the paths on the
logical network is 
, by Lemma 5.3. Thus,
this phase requires 
steps, with high probability. The
packets are routed in 
steps using the scheduling algorithm
from Section 2. Finally, packets destined
for bad nodes are deterministically routed from the good nodes to bad.
By an analysis similar to that of Lemma 5.4, this phase
also requires 
steps.