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 \((\varDelta +1)/2\)-approximation in unweighted graphs of maximum degree \(\varDelta \), which is best possible for 1-round distributed algorithms. For weighted graphs, it gives only a \((\varDelta +1)\)-approximation, but a simple modification results in an asymptotic expected \(0.529 (\varDelta +1)\)-approximation. This compares with a recent, more complex \(\varDelta \)-approximation [6], which holds deterministically.