  We consider the problem of computing a sequence of range minimum queries. We
assume a sequence of commands that contains values and queries. Our goal is to
quickly determine the minimum value that exists between the current position
and a previous position $i$. Range minimum queries are used as a sub-routine of
several algorithms, namely related to string processing. We propose a data
structure that can process these commands sequences. We obtain efficient
results for several variations of the problem, in particular we obtain $O(1)$
time per command for the offline version and $O(\alpha(n))$ amortized time for
the online version, where $\alpha(n)$ is the inverse Ackermann function and $n$
the number of values in the sequence. This data structure also has very small
space requirements, namely $O(\ell)$ where $\ell$ is the maximum number active
$i$ positions. We implemented our data structure and show that it is
competitive against existing alternatives. We obtain comparable command
processing time, in the nano second range, and much smaller space requirements.
