  We study the Maximum Independent Set problem for geometric objects given in
the data stream model. A set of geometric objects is said to be independent if
the objects are pairwise disjoint. We consider geometric objects in one and two
dimensions, i.e., intervals and disks. Let $\alpha$ be the cardinality of the
largest independent set. Our goal is to estimate $\alpha$ in a small amount of
space, given that the input is received as a one-pass stream. We also consider
a generalization of this problem by assigning weights to each object and
estimating $\beta$, the largest value of a weighted independent set. We
initialize the study of this problem in the turnstile streaming model
(insertions and deletions) and provide the first algorithms for estimating
$\alpha$ and $\beta$.
  For unit-length intervals, we obtain a $(2+\epsilon)$-approximation to
$\alpha$ and $\beta$ in poly$(\frac{\log(n)}{\epsilon})$ space. We also show a
matching lower bound. Combined with the $3/2$-approximation for insertion-only
streams by Cabello and Perez-Lanterno [CP15], our result implies a separation
between the insertion-only and turnstile model. For unit-radius disks, we
obtain a $\left(\frac{8\sqrt{3}}{\pi}\right)$-approximation to $\alpha$ and
$\beta$ in poly$(\log(n), \epsilon^{-1})$ space, which is closely related to
the hexagonal circle packing constant.
  We provide algorithms for estimating $\alpha$ for arbitrary-length intervals
under a bounded intersection assumption and study the parameterized space
complexity of estimating $\alpha$ and $\beta$, where the parameter is the ratio
of maximum to minimum interval length.
