Cardinality Estimation Meets Good-Turing

Abstract: Cardinality estimation algorithms receive a stream of elements whose order might be arbitrary, with possible repetitions, and return the number of distinct elements. Such algorithms usually seek to minimize the required storage and processing at the price of inaccuracy in their output. Real-world applications of these algorithms are required to process large volumes of monitored data, making it impractical to collect and analyze the entire input stream. In such cases, it is common practice to sample and process only a small part of the stream elements. This paper presents and analyzes a generic algorithm for combining every cardinality estimation algorithm with a sampling process. We show that the proposed sampling algorithm does not affect the estimator's asymptotic unbiasedness, and we analyze the sampling effect on the estimator's variance.