  We study streaming algorithms for the interval selection problem: finding a
maximum cardinality subset of disjoint intervals on the line. A deterministic
2-approximation streaming algorithm for this problem is developed, together
with an algorithm for the special case of proper intervals, achieving improved
approximation ratio of 3/2. We complement these upper bounds by proving that
they are essentially best possible in the streaming setting: it is shown that
an approximation ratio of $2 - \epsilon$ (or $3 / 2 - \epsilon$ for proper
intervals) cannot be achieved unless the space is linear in the input size. In
passing, we also answer an open question of Adler and Azar \cite{AdlerAzar03}
regarding the space complexity of constant-competitive randomized preemptive
online algorithms for the same problem.
