Streaming PTAS for Binary $\ell_0$-Low Rank Approximation

TL;DR

This paper presents the first constant-pass, polylog-space streaming PTAS algorithms for binary $ ext{ell}_0$-low rank approximation and binary $k$-means, leveraging their recently studied connection.

Contribution

It introduces the first constant-pass, polylog-space streaming PTAS algorithms for both problems, utilizing their connection to achieve this breakthrough.

Findings

First constant-pass streaming PTAS for binary $ ext{ell}_0$-low rank approximation

First constant-pass streaming PTAS for binary $k$-means

Polylogarithmic space complexity achieved for both problems

Abstract

We give a 3-pass, polylog-space streaming PTAS for the constrained binary $k$-means problem and a 4-pass, polylog-space streaming PTAS for the binary $\ell_0$-low rank approximation problem. The connection between the above two problems has recently been studied. We design a streaming PTAS for the former and use this connection to obtain streaming PTAS for the latter. This is the first constant pass, polylog-space streaming algorithm for either of the two problems.