This paper studies approximate distributed routing schemes on dynamic communication networks. The paper focuses on dynamic weighted general graphs where the vertices of the graph are fixed but the weights of the edges may change. Our main contribution concerns bounding the cost of adapting to dynamic changes. The update efficiency of a routing scheme is measured by the number of messages that need to be sent, following a weight change, in order to update the scheme. Our results indicate that the graph theoretic parameter governing the amortized message complexity of these updates is the local density D of the underlying graph, and specifically, this complexity is ${\tilde\Theta}(D)$ . The paper also establishes upper and lower bounds on the size of the databases required by the scheme at each site.

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