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Unformatted text preview: servation about ﬁnding shortestcost
paths in graphs, originally due to Bellman and Ford. Consider a node n in the network
and some destination d. Suppose that n hears from each of its neighbors, i, what its cost,
ci , to reach d is. Then, if n were to use the link ni as its route to reach d, the corresponding
cost would be ci + li , where li is the cost of the ni link. Hence, from n’s perspective, it
should choose the neighbor (link) for which the advertised cost plus the cost of the link
from n to that neighbor is smallest. More formally, the lowestcost path to use would be
via the neighbor j , where
j = arg min(ci + li ).
(18.1)
i The beautiful thing about this calculation is that it does not require the advertisements
from the different neighbors to arrive synchronously. They can arrive at arbitrary times,
and in any order; moreover, the integration step can run each time an advertisement arrives. The algorithm will eventually end up computing the right cost and ﬁnding the
correct route (i.e., it will converge).
Some care must be taken while implementing this algorithm, as outlined below: CHAPTER 18. NETWORK ROUTING  I 8 WITHOUT ANY FAILURES Figure 184: Periodic integration and advertisement steps at each node. 1. A node should update its cost and route if the new cost is smaller than the current
estimate, or if the cost of the route currently being used changes. One question you
might have is what the initial value of the cost should be before the node hears any
advertisements for a destination. clearly, it should be large, a number we’ll call “inﬁnity”. Later on, when we discuss failures, we will ﬁnd that “inﬁnity” for our simple
distancevector protocol can’t actually be all that large. Notice that “inﬁnity” does
needs to be larger than the cost of the longest minimumcost path in the network for
routing between any pair of nodes to work correctly, because a path cost of “inﬁnity”
between some two nodes means that there is no path between those two nodes.
2....
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 Fall '13
 HariBalakrishnan

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