Simple and Local Independent Set Approximation
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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 BCGS17, which holds deterministically.
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