Simple and Local Independent Set Approximation

TL;DR

This paper presents a simple, distributed, and streaming algorithm for approximating maximum independent sets in bounded-degree graphs, achieving tight bounds in unweighted cases and competitive ratios in weighted cases.

Contribution

It introduces a straightforward 1-round distributed algorithm with tight approximation guarantees, improving simplicity and efficiency over prior complex methods.

Findings

Achieves a tight (Δ+1)/2-approximation for unweighted graphs.

Provides a Δ-approximation for weighted graphs.

Modified algorithm yields a 0.529Δ-approximation, outperforming previous methods.

Abstract

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.