Single-message shuffled-model frequency estimation has optimal error about min(n^{1/4}, sqrt(B)); multi-message protocols achieve polylogarithmic error with polylogarithmic communication.
Locally private k-means clustering
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On the Power of Multiple Anonymous Messages
Single-message shuffled-model frequency estimation has optimal error about min(n^{1/4}, sqrt(B)); multi-message protocols achieve polylogarithmic error with polylogarithmic communication.