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We present A-GAP, a novel protocol for continuous monitoring of network state variables, which aims at achieving a given monitoring accuracy with minimal overhead. Network state variables are computed from device counters using aggregation functions, such as SUM, AVERAGE and MAX. The accuracy objective is expressed as the average estimation error. A-GAP is decentralized and asynchronous to achieve robustness and scalability. It executes on an overlay that interconnects management processes on the devices. On this overlay, the protocol maintains a spanning tree and updates the network state variables through incremental aggregation. Based on a stochastic model, it dynamically configures local filters that control whether an update is sent towards the root of the tree. We evaluate A-GAP through simulation using real traces and two different types of topologies of up to 650 nodes. The results show …