A Formal Analysis of the Count-Min Sketch with Conservative Updates

TL;DR

This paper provides a new theoretical analysis of the Count-Min Sketch with Conservative Updates, deriving bounds on estimation error that improve understanding and configuration of the algorithm for heavy-hitter detection.

Contribution

It introduces a novel analytical approach to derive bounds on CMS-CU's error, enhancing its theoretical understanding and practical configuration.

Findings

Derived new upper bounds on estimation error for CMS-CU

Improved accuracy estimates for heavy-hitter detection

Validated bounds on synthetic and real data traces

Abstract

Count-Min Sketch with Conservative Updates (CMS-CU) is a popular algorithm to approximately count items' appearances in a data stream. Despite CMS-CU's widespread adoption, the theoretical analysis of its performance is still wanting because of its inherent difficulty. In this paper, we propose a novel approach to study CMS-CU and derive new upper bounds on the expected value and the CCDF of the estimation error under an i.i.d. request process. Our formulas can be successfully employed to derive improved estimates for the precision of heavy-hitter detection methods and improved configuration rules for CMS-CU. The bounds are evaluated both on synthetic and real traces.