Sampling-based Estimation of the Number of Distinct Values in Distributed Environment

In data mining, estimating the number of distinct values (NDV) is a fundamental problem with various applications. Existing methods for estimating NDV can be broadly classified into two categories: i) scanning-based methods, which scan the entire data and maintain a sketch to approximate NDV; and ii) sampling-based methods, which estimate NDV using sampling data rather than accessing the entire data warehouse. Scanning-based methods achieve a lower approximation error at the cost of higher I/O and more time. Sampling-based estimation is preferable in applications with a large data volume and a permissible error restriction due to its higher scalability. However, while the sampling-based method is more effective on a single machine, it is less practical in a distributed environment with massive data volumes. For obtaining the final NDV estimators, the entire sample must be transferred throughout the distributed system, incurring a prohibitive communication cost when the sample rate is significant. This paper proposes a novel sketch-based distributed method that achieves sub-linear communication costs for distributed sampling-based NDV estimation under mild assumptions. Our method leverages a sketch-based algorithm to estimate the sample's frequency of frequency in the distributed streaming model, which is compatible with most classical sampling-based NDV estimators. Additionally, we provide theoretical evidence for our method's ability to minimize communication costs in the worstcase scenario. Extensive experiments show that our method saves orders of magnitude in communication costs compared to existing sampling- and sketch-based methods.