  Semidefinite programming is an important tool to tackle several problems in
data science and signal processing, including clustering and community
detection. However, semidefinite programs are often slow in practice, so speed
up techniques such as sketching are often considered. In the context of
community detection in the stochastic block model, Mixon and Xie
\cite{mixon2020sketching} have recently proposed a sketching framework in which
a semidefinite program is solved only on a subsampled subgraph of the network,
giving rise to significant computational savings. In this short paper, we
provide a positive answer to a conjecture of Mixon and Xie about the
statistical limits of this technique for the stochastic block model with two
balanced communities.
