Streaming PTAS for Binary ${\mathrm{\ell }}_0$-Low Rank Approximation

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 ${\mathrm{\ell }}_0$-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.