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We consider the problem of dynamic aggregation of inputs over a large fixed graph. A dynamic aggregation algorithm must continuously compute the result of a given aggregation function over a dynamically changing set of inputs. To be efficient, such an algorithm should refrain from sending messages when the inputs do not change, and should perform local communication whenever possible. We present an instance-based lower bound on the efficiency of such algorithms, and provide two algorithms matching this bound. The first, MultI-LEAG, re-samples the inputs at intervals that are proportional to the graph size, achieving quiescence between samplings, and is extremely message efficient. The second, DynI-LEAG, more closely monitors the aggregate value by sampling it more frequently, at the cost of slightly higher message complexity.