Bias-Aware Sketches

Count-Sketch [6] and Count-Median [11] are two widely used sketching algorithms for processing large-scale distributed and streaming datasets, such as finding frequent elements, computing frequency moments, performing point queries, etc. The errors of Count-Sketch and Count-Median are expressed in terms of the sum of coordinates of the input vector excluding those largest ones, or, the mass on the tail of the vector. Thus, the precondition for these algorithms to perform well is that the mass on the tail is small, which is, however, not always the case – in many real-world datasets the coordinates of the input vector have a non-zero bias, which will generate a large mass on the tail. In this paper we propose linear sketches that are bias-aware. They can be used as substitutes to Count-Sketch and Count-Median, and achieve strictly better error guarantees. We also demonstrate their practicality by an extensive experimental evaluation on both real and synthetic datasets.