  A set of intervals is independent when the intervals are pairwise disjoint.
In the interval selection problem we are given a set $\mathbb{I}$ of intervals
and we want to find an independent subset of intervals of largest cardinality.
Let $\alpha(\mathbb{I})$ denote the cardinality of an optimal solution. We
discuss the estimation of $\alpha(\mathbb{I})$ in the streaming model, where we
only have one-time, sequential access to the input intervals, the endpoints of
the intervals lie in $\{1,...,n \}$, and the amount of the memory is
constrained.
  For intervals of different sizes, we provide an algorithm in the data stream
model that computes an estimate $\hat\alpha$ of $\alpha(\mathbb{I})$ that, with
probability at least $2/3$, satisfies $\tfrac 12(1-\varepsilon)
\alpha(\mathbb{I}) \le \hat\alpha \le \alpha(\mathbb{I})$. For same-length
intervals, we provide another algorithm in the data stream model that computes
an estimate $\hat\alpha$ of $\alpha(\mathbb{I})$ that, with probability at
least $2/3$, satisfies $\tfrac 23(1-\varepsilon) \alpha(\mathbb{I}) \le
\hat\alpha \le \alpha(\mathbb{I})$. The space used by our algorithms is bounded
by a polynomial in $\varepsilon^{-1}$ and $\log n$. We also show that no better
estimations can be achieved using $o(n)$ bits of storage.
  We also develop new, approximate solutions to the interval selection problem,
where we want to report a feasible solution, that use $O(\alpha(\mathbb{I}))$
space. Our algorithms for the interval selection problem match the optimal
results by Emek, Halld{\'o}rsson and Ros{\'e}n [Space-Constrained Interval
Selection, ICALP 2012], but are much simpler.
