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One of the most prominent and comprehensive ways of data collection in sensor networks is to periodically extract raw sensor readings. This way of data collection enables complex analysis of data, which may not be possible with in-network aggregation or query processing. However, this flexibility in data analysis comes at the cost of power consumption. In this paper, we develop ASAP, which is an adaptive sampling approach to energy-efficient periodic data collection in sensor networks. The main idea behind ASAP is to use a dynamically changing subset of the nodes as samplers such that the sensor readings of the sampler nodes are directly collected, whereas the values of the nonsampler nodes are predicted through the use of probabilistic models that are locally and periodically constructed. ASAP can be effectively used to increase the network lifetime while keeping the quality of the collected data high in scenarios where either the spatial density of the network deployment is superfluous, which is relative to the required spatial resolution for data analysis, or certain amount of data quality can be traded off in order to decrease the power consumption of the network. The ASAP approach consists of three main mechanisms: First, sensing-driven cluster construction is used to create clusters within the network such that nodes with close sensor readings are assigned to the same clusters. Second, correlation-based sampler selection and model derivation are used to determine the sampler nodes and to calculate the parameters of the probabilistic models that capture the spatial and temporal correlations among the sensor readings. Last, adaptive data collection and model-based prediction are used to minimize the number of messages used to extract data from the network. A unique feature of ASAP is the use of in-network schemes, as opposed to the protocols requiring centralized control, to select and dynamically refine the subset of the sensor nodes serving as samplers and to - - adjust the value prediction models used for nonsampler nodes. Such runtime adaptations create a data collection schedule, which is self-optimizing in response to the changes in the energy levels of the nodes and environmental dynamics. We present simulation-based experimental results and study the effectiveness of ASAP under different system settings.