TreeSensing: Linearly Compressing Sketches with Flexibility.

A Sketch is an excellent probabilistic data structure, which records the approximate statistics of data streams. Linear additivity is an important property of sketches. This paper studies how to keep the linear property after sketch compression. Most existing compression methods do not keep the linear property. We propose TreeSensing, an accurate, efficient, and flexible framework to linearly compress sketches. In TreeSensing, we first separate a sketch into two parts according to counter values. For the sketch with small counters, we propose a technique called TreeEncoding to compress it into a hierarchical structure. For the sketch with large counters, we propose a technique called SketchSensing to compress it using compressive sensing. We theoretically analyze the accuracy of TreeSensing. We use TreeSensing to compress 7 sketches and conduct two end-to-end experiments: distributed measurement and distributed machine learning. Experimental results show that TreeSensing outperforms prior art on both accuracy and efficiency, which achieves up to 100× smaller error and 5.1× higher speed than state-of-the-art Cluster-Reduce. All related codes are open-sourced.