Towards Optimal Moment Estimation in Streaming and Distributed Models

@inproceedings{Jayaram2019TowardsOM,
title={Towards Optimal Moment Estimation in Streaming and Distributed Models},
author={Rajesh Jayaram and David P. Woodruff},
booktitle={APPROX-RANDOM},
year={2019}
}

One of the oldest problems in the data stream model is to approximate the $p$-th moment $\|\mathcal{X}\|_p^p = \sum_{i=1}^n |\mathcal{X}_i|^p$ of an underlying vector $\mathcal{X} \in \mathbb{R}^n$, which is presented as a sequence of poly$(n)$ updates to its coordinates. Of particular interest is when $p \in (0,2]$. Although a tight space bound of $\Theta(\epsilon^{-2} \log n)$ bits is known for this problem when both positive and negative updates are allowed, surprisingly there is still a gap… Expand