Finding Frequent Items in Data Streams

Finding Frequent Items in Data Streams

| Moses Charikar, Kevin Chen, and Martin Farach-Colton
This paper presents a 1-pass algorithm for estimating the most frequent items in a data stream using very limited storage space. The algorithm uses a novel data structure called a COUNT SKETCH, which allows for efficient estimation of item frequencies. The COUNT SKETCH data structure is designed to handle the problem of finding the most frequent items in a stream with high accuracy and low space complexity. The algorithm achieves better space bounds than previous methods for many natural distributions of item frequencies. Additionally, the algorithm can be adapted to find items with the largest frequency changes between two data streams, a problem that has not been previously studied in the literature. The COUNT SKETCH algorithm works by maintaining a set of hash functions and counters that allow for the estimation of item frequencies. The algorithm processes each item in the stream, updating the counters based on the hash functions. The estimated frequencies are then used to determine the top k most frequent items. The algorithm ensures that the estimated frequencies are accurate within a certain error margin, which is determined by the parameter ε. The algorithm also provides a guarantee that all items with frequencies significantly higher than the kth most frequent item will be included in the output list. The COUNT SKETCH algorithm is shown to be effective for a wide range of distributions, including Zipfian distributions, where the frequency of items decreases as their rank increases. The algorithm's space requirements are analyzed for these distributions, and it is shown that the algorithm outperforms the sampling-based approach in terms of space efficiency. The algorithm can also be adapted to find items with the largest frequency changes between two streams, which is achieved by processing both streams and computing the difference in their sketches. This leads to a 2-pass algorithm for finding items with the largest frequency changes. The paper concludes with a comparison of the COUNT SKETCH algorithm with the sampling-based approach, highlighting the advantages of the COUNT SKETCH algorithm in terms of space efficiency and accuracy. The algorithm is shown to be particularly effective for large data streams and for distributions where the frequencies of items follow a certain pattern. The algorithm's ability to handle large data streams with limited storage space makes it a valuable tool for applications such as search engines, where the goal is to find the most frequent queries in a stream of search requests.This paper presents a 1-pass algorithm for estimating the most frequent items in a data stream using very limited storage space. The algorithm uses a novel data structure called a COUNT SKETCH, which allows for efficient estimation of item frequencies. The COUNT SKETCH data structure is designed to handle the problem of finding the most frequent items in a stream with high accuracy and low space complexity. The algorithm achieves better space bounds than previous methods for many natural distributions of item frequencies. Additionally, the algorithm can be adapted to find items with the largest frequency changes between two data streams, a problem that has not been previously studied in the literature. The COUNT SKETCH algorithm works by maintaining a set of hash functions and counters that allow for the estimation of item frequencies. The algorithm processes each item in the stream, updating the counters based on the hash functions. The estimated frequencies are then used to determine the top k most frequent items. The algorithm ensures that the estimated frequencies are accurate within a certain error margin, which is determined by the parameter ε. The algorithm also provides a guarantee that all items with frequencies significantly higher than the kth most frequent item will be included in the output list. The COUNT SKETCH algorithm is shown to be effective for a wide range of distributions, including Zipfian distributions, where the frequency of items decreases as their rank increases. The algorithm's space requirements are analyzed for these distributions, and it is shown that the algorithm outperforms the sampling-based approach in terms of space efficiency. The algorithm can also be adapted to find items with the largest frequency changes between two streams, which is achieved by processing both streams and computing the difference in their sketches. This leads to a 2-pass algorithm for finding items with the largest frequency changes. The paper concludes with a comparison of the COUNT SKETCH algorithm with the sampling-based approach, highlighting the advantages of the COUNT SKETCH algorithm in terms of space efficiency and accuracy. The algorithm is shown to be particularly effective for large data streams and for distributions where the frequencies of items follow a certain pattern. The algorithm's ability to handle large data streams with limited storage space makes it a valuable tool for applications such as search engines, where the goal is to find the most frequent queries in a stream of search requests.
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