Simple and Local Independent Set Approximation

We bound the performance guarantees that follow from Turán-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 $(Δ+1)/2$-approximation in unweighted graphs of maximum degree $Δ$, which is best possible for 1-round distributed algorithms. For weighted graphs, it gives only a $Δ$-approximation, but a simple modification results in an asymptotic expected $0.529 Δ$-approximation. This compares with a recent, more complex $Δ$-approximation~\cite{BCGS17}, which holds deterministically.