**Lee, G. M.**, Liu, H., Yoon, Y., and Zhang, Y. (2005). Improving Sketch Reconstruction Accuracy Using Linear Least Square Method, In *Proceedings of Internet Measurement Conference (***IMC 2005**), Berkeley, California.

**IMC 2005**)

- IMC is a premier conference in the network measurement area (h5-index: 37)

Sketch is a sublinear space data structure that allows one to approximately reconstruct the value associated with any given key in an input data stream. It is the basis for answering a number of fundamental queries on data streams, such as range queries, finding quantiles, frequent items, etc. In the networking context, sketch has been applied to identifying heavy hitters and changes, which is critical for traffic monitoring, accounting, and network anomaly detection.

In this paper, we propose a novel approach called *lsquare* to significantly improve the reconstruction accuracy of the sketch data structure. Given a sketch and a set of keys, we estimate the values associated with these keys by constructing a linear system and finding the optimal solution for the system using linear least squares method. We use a large amount of real Internet traffic data to evaluate *lsquare* against *countmin*, the state-of-the-art sketch scheme. Our results suggest that given the same memory requirement, *lsquare* achieves much better reconstruction accuracy than *countmin*. Alternatively, given the same reconstruction accuracy, *lsquare* requires significantly less memory. This clearly demonstrates the effectiveness of our approach.