422 A Distance Vector Routing Algorithm

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While the LS algorithm is an algorithm using global information, the distance vector (DV) algorithm is iterative, asynchronous, and distributed It is distributed in that each node receives some information from one or more of its directly attached neighbors, performs a

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Point-to-Point Routing Algorithms

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calculation, and may then distribute the results of its calculation back to its neighbors It is iterative in that this process continues on until no more information is exchanged between neighbors (Interestingly, we will see that the algorithm is self terminating -- there is no "signal" that the computation should stop; it just stops) The algorithm is asynchronous in that it does not require all of the nodes to operate in lock step with each other We'll see that an asynchronous, iterative, self terminating, distributed algorithm is much more "interesting" and "fun" than a centralized algorithm The principal data structure in the DV algorithm is the distance table maintained at each node Each node's distance table has a row for each destination in the network and a column for each of its directly attached neighbors Consider a node X that is interested in routing to destination Y via its directly attached neighbor Z Node X's distance table entry, Dx(Y,Z) is the sum of the cost of the direct one hop link between X and Z, c(X,Z), plus neighbor Z's currently known minimum cost path from itself (Z) to Y That is: Dx(Y,Z) = c(X,Z) + minw{Dz(Y,w)} (4-1)

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The minw term in equation 4-1 is taken over all of Z's directly attached neighbors (including X, as we shall soon see) Equation 4-1 suggests the form of the neighbor-to-neighbor communication that will take place in the DV algorithm -- each node must know the cost of each of its neighbors minimum cost path to each destination Thus, whenever a node computes a new minimum cost to some destination, it must inform its neighbors of this new minimum cost Before presenting the DV algorithm, let's consider an example that will help clarify the meaning of entries in the distance table Consider the network topology and the distance table shown for node E in Figure 42-3 This is the distance table in node E once the Dv algorithm has converged Let's first look at the row for destination A

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Clearly the cost to get to A from E via the direct connection to A has a cost of 1 Hence DE(A,A) = 1 Let's now consider the value of DE(A,D) - the cost to get from E to A, given that the first step along the path is D In this case, the distance table entry is the cost to get from E to D (a cost of 2) plus whatever the minimum cost it is to get from D to A Note that the minimum cost from D to A is 3 -- a path that passes right back through E! Nonetheless, we record the fact that the minimum cost from E to A given that the first step is via D has a cost of 5 We're left, though, with an uneasy feeling that the fact the path from E via D loops back through E may be the source of problems down the road (it will!) Similarly, we find that the distance table entry via neighbor B is DE(A,B) = 14 Note that the cost is not 15 (why )

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Figure 42-3: A distance table example

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A circled entry in the distance table gives the cost of the least cost path to the corresponding destination (row) The column with the circled entry identifies the next node along the least cost path to the destination Thus, a node's routing table (which indicates which outgoing link should be used to forward packets to a given destination) is easily constructed from the node's distance table In discussing the distance table entries for node E above, we informally took a global view, knowing the costs of all links in the network The distance vector algorithm we will now present is decentralized and does not use such global information Indeed, the only information a node

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