Stream Processing is a crucial element for the Edge Computing paradigm, in which large amount of devices generate data at the edge of the network. This data needs to be aggregated and processed on-the-move across different layers before reaching the Cloud. Therefore, defining Stream Processing services that adapt to different levels of resource availability is of paramount importance. In this context, Stream Processing frameworks need to combine efficient algorithms with low computational complexity to manage sliding windows, with the ability to adjust resource demands for different deployment scenarios, from very low capacity edge devices to virtually unlimited Cloud platforms. The Approximate Computing paradigm provides improved performance and adaptive resource demands in data analytics, at the price of introducing some level of inaccuracy that can be calculated. In this paper we present the Approximate and Amortized Monoid Tree Aggregator (A2MTA). It is, to our knowledge, the first general purpose sliding window programable framework that combines constant-time aggregations with error bounded approximate computing techniques. It is very suitable for adverse stream processing environments, such as resource scarce multi-tenant edge computing. The framework can compute aggregations over multiple data dimensions, setting error bounds on any of them, and has been designed to support decoupling computation and data storage through the use of distributed Key-Value Stores to keep window elements and partial aggregations.

The fast evolution of data analytics platforms has resulted in an increasing demand for real-time data stream processing. From Internet of Things applications to the monitoring of telemetry generated in large data centers, a common demand for currently emerging scenarios is the need to process vast amounts of data with low latencies, generally performing the analysis process as close to the data source as possible. Stream processing platforms are required to be malleable and absorb spikes generated by fluctuations of data generation rates. Data is usually produced as time series that have to be aggregated using multiple operators, being sliding windows one of the most common abstractions used to process data in real-time. To satisfy the above-mentioned demands, efficient stream processing techniques that aggregate data with minimal computational cost need to be developed. In this paper we present the Monoid Tree Aggregator general sliding window aggregation framework, which seamlessly combines the following features: amortized$O(1)$time complexity and a worst-case of$O(\log {n})$between insertions; it provides both a window aggregation mechanism and a window slide policy that are user programmable; the enforcement of the window sliding policy exhibits amortized$O(1)$computational cost for single evictions and supports bulk evictions with cost$O(\log {n})$; and it requires a local memory space of$O(\log {n})$. The framework can compute aggregations over multiple data dimensions, and has been designed to support decoupling computation and data storage through the use of distributedKey-Value Storesto keep window elements and partial aggregations.