# Space Complexity of Euclidean Clustering

arXiv: https://arxiv.org/abs/2403.02971 · HTML: https://mlsanity.com/paper/2403.02971/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [On Approximability of ℓ22 Min-Sum Clustering](https://mlsanity.com/paper/2412.03332/) (2024)

## Abstract (arXiv)

The (k, z)-Clustering problem in Euclidean space ℝd has been extensively studied. Given the scale of data involved, compression methods for the Euclidean (k, z)-Clustering problem, such as data compression and dimension reduction, have received significant attention in the literature. However, the space complexity of the clustering problem, specifically, the number of bits required to compress the cost function within a multiplicative error varepsilon, remains unclear in existing literature. This paper initiates the study of space complexity for Euclidean (k, z)-Clustering and offers both upper and lower bounds. Our space bounds are nearly tight when k is constant, indicating that storing a coreset, a well-known data compression approach, serves as the optimal compression scheme. Furthermore, our lower bound result for (k, z)-Clustering establishes a tight space bound of Theta( n d ) for terminal embedding, where n represents the dataset size. Our technical approach leverages new geometric insights for principal angles and discrepancy methods, which may hold independent interest.