A Minimal Variance Estimator for the Cardinality of Big Data Set Intersection

Reuven Cohen (Technion);Liran Katzir (Technion);Aviv Yehezkel (Technion)

Abstract

In recent years there has been a growing interest in developing ``streaming algorithms’’ for efficient processing and querying of continuous data streams. These algorithms seek to provide accurate results while minimizing the required storage and the processing time, at the price of a small inaccuracy in their output. A fundamental query of interest is the intersection size of two big data streams. This problem arises in many different application areas, such as network monitoring, database systems, data integration and information retrieval. In this paper we develop a new algorithm for this problem, based on the Maximum Likelihood (ML) method. We show that this algorithm outperforms all known schemes in terms of the estimation’s quality (lower variance) and that it asymptotically achieves the optimal variance.