To monitor critical infrastructure, high quality sensors sampled at a high frequency are increasingly installed. However, due to the big amounts of data produced, only simple aggregates are stored. This removes outliers and hides fluctuations that could indicate problems. As a solution we propose compressing time series with dimensions using a model-based method we name Multi-model Group Compression (MMGC). MMGC adaptively compresses groups of correlated time series with dimensions using an extensible set of models within a user-defined error bound (possibly zero). To partition time series into groups, we propose a set of primitives for efficiently describing correlation for data sets of varying sizes. We also propose efficient query processing algorithms for executing multi-dimensional aggregate queries on models instead of data points. Last, we provide an open-source implementation of our methods as extensions to the model-based Time Series Management System (TSMS) ModelarDB. ModelarDB interfaces with the stock versions of Apache Spark and Apache Cassandra and thus can reuse existing infrastructure. Through an evaluation we show that, compared to widely used systems, our extended ModelarDB provides up to 11 times faster ingestion due to high compression, 65 times better compression due to the adaptivity of MMGC, 92 times faster aggregate queries as they are executed on models, and close to linear scalability while also being extensible and supporting online query processing.
 The increasing use of sensor technology for various monitoring applications (e.g. air-pollution, traffic, climate-change, etc.) has led to an unprecedented volume of streaming data that has to be efficiently aggregated, stored and retrieved. Real-time model-based data approximation and filtering is a common solution for reducing the storage (and communication) overhead. However, the selection of the most efficient model depends on the characteristics of the data stream, namely rate, burstiness, data range, etc., which cannot be always known a priori for (mobile) sensors and they can even dynamically change. In this paper, we investigate the innovative concept of efficiently combining multiple approximation models in real-time. Our approach dynamically adapts to the properties of the data stream and approximates each data segment with the most suitable model. As experimentally proved, our multi-model approximation approach always produces fewer or equal data segments than those of the best individual model, and thus provably achieves higher data compression ratio than individual linear models. Time-series data is increasingly collected in many domains. One example is the smart electricity infrastructure, which generates huge volumes of such data from sources such as smart electricity meters. Although today these data are used for visualization and billing in mostly 15-min resolution, its original temporal resolution frequently is more fine-grained, e.g., seconds. This is useful for various analytical applications such as short-term forecasting, disaggregation and visualization. However, transmitting and storing huge amounts of such fine-grained data are prohibitively expensive in terms of storage space in many cases. In this article, we present a compression technique based on piecewise regression and two methods which describe the performance of the compression. Although our technique is a general approach for time-series compression, smart grids serve as our running example and as our evaluation scenario. Depending on the data and the use-case scenario, the technique compresses data by ratios of up to factor 5,000 while maintaining its usefulness for analytics. The proposed technique has outperformed related work and has been applied to three real-world energy datasets in different scenarios. Finally, we show that the proposed compression technique can be implemented in a state-of-the-art database management system. The volume of time series stream data grows rapidly in various applications. To reduce the storage, transmission and processing costs of time series data, segmentation and approximation is a common approach. In this paper, we propose a novel online segmentation algorithm that approximates time series by a set of different types of candidate functions (polynomials of different orders, exponential functions, etc.) and adaptively chooses the most compact one as the pattern of the time series changes. We call this algorithm the Adaptive Approximation (AA) algorithm. The AA algorithm incrementally narrows the feasible coefficient spaces (FCS) of candidate functions in coefficient coordinate systems to make each segment as long as possible given an error bound on each data point. We propose an algorithm called the FCS algorithm for the incremental computation of the feasible coefficient spaces. We further propose a mapping based index for similarity searches on the approximated time series. Experimental results show that our AA algorithm generates more compact approximations of the time series with lower average errors than the state-of-the-art algorithm, and our indexing method processes similarity searches on the approximated time series efficiently.