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Difficulty: Hard
Category: Algorithms & Data Structures
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Topics: algorithms, data-structures, probability, estimation, cardinality
You are designing a real-time analytics system to track the number of unique users visiting a popular website. Due to memory constraints, you decide to use the HyperLogLog algorithm. The algorithm utilizes $m$ registers to approximate the cardinality (number of distinct elements). What is the approximate standard error of the HyperLogLog algorithm's cardinality estimation, expressed as a function of $m$?
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