Simple and Local Independent Set Approximation

We bound the performance guarantees that follow from Tur\'an-like bounds for unweighted and weighted independent sets in bounded-degree graphs. In particular, a randomized approach of Boppana forms a simple 1-round distributed algorithm, as well as a streaming and preemptive online algorithm. We show it gives a tight $(\Delta+1)/2$-approximation in unweighted graphs of maximum degree $\Delta$, which is best possible for 1-round distributed algorithms. For weighted graphs, it gives only a $\Delta$-approximation, but a simple modification results in an asymptotic expected $0.529 \Delta$-approximation. This compares with a recent, more complex $\Delta$-approximation~\cite{BCGS17}, which holds deterministically.