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Unformatted text preview: asy to see that if the minimum-cost path has length 1 (i.e., 1 hop), then the algorithm
ﬁnds it correctly. Now suppose that the algorithm correctly computes the minimum-cost SECTION 18.5. A SIMPLE LINK-STATE ROUTING PROTOCOL 9 path from a node s to any destination for which the minimum-cost path is ≤ hops. Now
consider a destination, d, whose minimum-cost path is of length + 1. It is clear that this
path may be written as s, t, . . . , d, where t is a neighbor of s and the sub-path from t to d
has length . By the inductive assumption, the sub-path from t to d is a path of length and
therefore the algorithm must have correctly found it. The Bellman-Ford integration step at
s processes all the advertisements from s’s neighbors and picks the route whose link cost
plus the advertised path cost is smallest. Because of this step, and the assumption that the
minimum-cost path has length + 1, the path s, t, . . . , d must be a minimum-cost route that
is correctly computed by the algorithm. This completes the proof of correctness.
How well does this protocol work? In the absence of failures, and for small networks,
it’s quite a good protocol. It does not consume too much network bandwidth, though the
size of the advertisements grows linearly with the size of the network. How long does it
take for the protocol to converge, assuming no packet losses or other failures occur? The
next lecture will discuss what it means for a protocol to “converge”; brieﬂy, what we’re
asking here is the time it takes for each of the nodes to have the correct routes to every other
destination. To answer this question, observe that after every integration step, assuming
that advertisements and integration steps occur at the same frequency, every node obtains
information about potential minimum-cost paths that are one hop longer compared to the
previous integration step. This property implies that after H steps, each node will have
correct minimum-cost paths to all destinations for...
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.
- Fall '13