Breakthrough in Optimal Space Complexity for Frequency Moment Estimation
2024-12-29
A paper by Mark Braverman and Or Zamir proves an optimal space lower bound of Ω(log(nε²)/ε²) for estimating frequency moments, where ε = Ω(1/√n). This research solves a long-standing problem in computational complexity, matching the classic Alon-Matias-Szegedy upper bound within a certain range. For smaller values of ε, the paper also introduces an improved algorithm that further refines the space complexity of frequency moment estimation. This breakthrough provides crucial theoretical guidance for stream data processing and algorithm design.
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