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An Optimal Algorithm for the Distinct Elements Problem Inspired by Bar-Yossef et al. (2002)

This paper presents an efficient algorithm for solving the Distinct Elements Problem, leveraging insights from Bar-Yossef et al. (2002). We explore the theoretical underpinnings of the algorithm, which addresses the challenge of identifying distinct elements within a given dataset, optimizing for both time and space complexity. By innovatively applying probabilistic techniques, our algorithm ensures a high accuracy rate when estimating unique elements while minimizing computational resources. This research contributes to the field of theoretical computer science and enhances algorithms used in data analysis.

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An Optimal Algorithm for the Distinct Elements Problem Inspired by Bar-Yossef et al. (2002)

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  1. An Optimal Algorithm for the Distinct Elements Problem Inspired by [Bar-Yossef et al. 2002] 11724 17 9 2 5 1 1 4 6 1/ε2 1 2 3 h:{1,…,n} {1,…,log n} 4 Pr[h(i) = j] = 1/2j … 5 … log n 4 3 4 3 4 5 2 g:{1,…,n} {1,…,1/ε2} MIT Computer Science and Artificial Intelligence Laboratory, Theory of Computation Group

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