  In this paper, we consider a randomized greedy algorithm for independent sets
in $r$-uniform $d$-regular hypergraphs $G$ on $n$ vertices with girth $g$. By
analyzing the expected size of the independent sets generated by this
algorithm, we show that $\alpha(G)\geq (f(d,r)-\epsilon(g,d,r))n$, where
$\epsilon(g,d,r)$ converges to $0$ as $g\rightarrow\infty$ for fixed $d$ and
$r$, and $f(d,r)$ is determined by a differential equation. This extends
earlier results of Gamarnik and Goldberg for graphs. We also prove that when
applying this algorithm to uniform linear hypergraphs with bounded degree, the
size of the independent sets generated by this algorithm concentrate around the
mean asymptotically almost surely.
