"Those who cannot remember the past, are condemned to repeat it. " (Philosopher George Santayana) In this paper we show that keeping track of history enables significant improvements in the communication complexity of dynamic networks protocols. We improve the communication complexity for solving any graph problem from \Theta(E) to \Theta(V), thus achieving the lower bound. Moreover, O(V) is also our amortized complexity of solving any function (not only graph functions) defined on the local inputs of the nodes. This proves, for the first time, that amortized communication complexity, i.e. incremental cost of adapting to a single topology change, can be smaller than the communication complexity of solving the problem from scratch. This also has a practical importance: in real networks the topology and the local inputs of the nodes change. The first stage in our solution is a communication optimal maintenance of a spanning tree in a dynamic network. The second stage is the optimal maintenance of replicas of databases. An important example of this task is the problem of updating the description of
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