The paper introduces the Count-Min Sketch (CMS), a new data structure designed for summarizing data streams. CMS allows for approximate answers to fundamental queries such as point, range, and inner product queries, as well as solving more complex problems like finding quantiles and frequent items. The key advantages of CMS include: 1. **Space Efficiency**: The space used is proportional to \(1/\varepsilon\), significantly improving over previous methods that required \(1/\varepsilon^2\) space. 2. **Fast Updates**: The update time is sublinear in the size of the sketch, making it suitable for high-performance monitoring applications. 3. **Simplicity**: CMS uses only pairwise independent hash functions, which are simple to construct and implement. 4. **Versatility**: CMS can be used for multiple queries and applications, with explicit and small constants. 5. **Practicality**: The approach is simple and likely to find many practical applications, including hardware solutions. The paper also discusses the preliminaries of data streams, including the types of queries (point, range, inner product) and the importance of these queries in various applications. It provides detailed analyses and proofs for the accuracy and efficiency of CMS in answering these queries. Additionally, the paper explores applications of CMS in finding quantiles and heavy hitters in data streams, showing significant improvements over previous methods in terms of space and time complexity.The paper introduces the Count-Min Sketch (CMS), a new data structure designed for summarizing data streams. CMS allows for approximate answers to fundamental queries such as point, range, and inner product queries, as well as solving more complex problems like finding quantiles and frequent items. The key advantages of CMS include: 1. **Space Efficiency**: The space used is proportional to \(1/\varepsilon\), significantly improving over previous methods that required \(1/\varepsilon^2\) space. 2. **Fast Updates**: The update time is sublinear in the size of the sketch, making it suitable for high-performance monitoring applications. 3. **Simplicity**: CMS uses only pairwise independent hash functions, which are simple to construct and implement. 4. **Versatility**: CMS can be used for multiple queries and applications, with explicit and small constants. 5. **Practicality**: The approach is simple and likely to find many practical applications, including hardware solutions. The paper also discusses the preliminaries of data streams, including the types of queries (point, range, inner product) and the importance of these queries in various applications. It provides detailed analyses and proofs for the accuracy and efficiency of CMS in answering these queries. Additionally, the paper explores applications of CMS in finding quantiles and heavy hitters in data streams, showing significant improvements over previous methods in terms of space and time complexity.