We consider the problem of collectively approximating a set of sensor signals using the least amount of space so that any individual signal can be eﬃciently reconstructed within a given maximum (L∞) error ε. The problem arises naturally in applications that need to collect large amounts of data from multiple concurrent sources, such as sensors, servers and network routers, and archive them over a long period of time for oﬄine data mining. We present GAMPS, a general framework that addresses this problem by combining several novel techniques. First, it dynamically groups multiple signals together so that signals within each group are correlated and can be maximally compressed jointly. Second, it appropriately scales the amplitudes of diﬀerent signals within a group and compresses them within the maximum allowed reconstruction error bound. Our schemes are polynomial time O(α,β) approximation schemes, meaning that the maximum (L∞) error is at most αε and it uses at most β times the optimal memory. Finally, GAMPS maintains an index so that various queries can be issued directly on compressed data. Our experiments on several real-world sensor datasets show that GAMPS signiﬁcantly reduces space without compromising the quality of search and query.