Despite the importance of providing quick responsiveness to user requests for online services, such request processing is very resource expensive when dealing with large-scale service datasets. These often exceed the service providers' budget when services are deployed on a cloud, in which resources are charged in monetary terms. Providing approximate processing results in request processing is a feasible solution for such problem that trades off result correctness (e.g. prediction or query accuracy) for response time reduction. However, existing techniques in this area either use parts of datasets or skip expensive computations to produce approximate results, thus resulting in large losses in result correctness on a tight resource budget. In this paper, we propose Synopsis-based Approximate Request Processing (SARP), a SARP framework to produce approximate results with small correctness losses even using small amount of resources. To achieve this, SARP conducts computations over synopses, which aggregate the statistical information of the entire service dataset at different approximation levels, based on two key ideas: (1) offline synopsis management that generates and maintains a set of synopses that represent the aggregation information of the dataset at different approximation levels.(2) Online synopsis selection that considers both the current resource allocation and the workload status so as to select the synopsis with the maximal length that can be processed within the B Rui Han 123 Int J Parallel Prog required response time. We demonstrate the effectiveness of our approach by testing the recommendation services in e-commerce sites using a large, real-world dataset. Using prediction accuracy as the result correctness metric, the results demonstrate: (i) SARP achieves significant response time reduction with very small correctness losses compared to the exact processing results; (ii) using the same processing time, SARP demonstrates a considerable reduction in correctness loss compared to existing approximation techniques.