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In this paper, we consider a randomized greedy algorithm for independent setsin $r$-uniform $d$-regular hypergraphs $G$ on $n$ vertices with girth $g$. Byanalyzing the expected size of the independent sets generated by thisalgorithm, 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 extendsearlier results of Gamarnik and Goldberg for graphs. We also prove that whenapplying this algorithm to uniform linear hypergraphs with bounded degree, thesize of the independent sets generated by this algorithm concentrate around themean asymptotically almost surely.

Randomized greedy algorithm for independent sets in regular uniform hypergraphs with large girth