  Given the query string of length $m$, we explore a parallel query in a static
suffix tree based data structure for $p \ll n$, where $p$ is the number of
processors and $n$ is the length of the text. We present three results on CREW
PRAM. The parallel query in the suffix trie requires $O(m + p)$ work, $O(m/p +
\lg p)$ time and $O(n^2)$ space in the worst case. We extend the same technique
to the suffix tree where we show it is, by design, inherently sequential in the
worst case. Finally we perform the parallel query using an interleaved approach
and achieve $O(m \lg p)$ work, $O(\frac{m}{p} \lg p)$ time and $O(n \lg p)$
space in the worst case.
