In this work we consider the Maximal Independent Set (MIS) problem and the metric Steiner Forest problem in the sublinear time setting, under the adjacency/distance matrix query model. First, we give an algorithm that estimates the size of an MIS up to a multiplicative factor of $(1+\eps)$ using $\tO(n^{4/3}/\eps^2)$ queries. This improves the best previous algorithm by Mahabadi, Roghani, Tarnawski, and Vakilian (SODA 2026), which had a query complexity of $\tO(n^{3/2}/\eps^2)$. Via a reduction from that work, this would automatically imply the same improvement for the problem of estimating the metric Steiner Forest cost up to an $O(\log n)$ factor. However, as our second contribution, we consider the Steiner Forest problem directly and provide an algorithm with $\tO(n)$ query complexity that is very simple and does not proceed via MIS.

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