Distributed fractional local ratio and independent set approximation

Abstract

We consider the Maximum Weight Independent Set problem, with a focus on obtaining good approximations for graphs of small maximum degree Δ. We give deterministic local algorithms running in time $\mathrm{poly}(\Delta ,\log n)$ that come close to matching the best centralized results known and improve the previous distributed approximations by a factor of about 2. More precisely, we obtain approximations below $\frac{\Delta +1/2}{2}$, and a further improvement to $8/5+\epsilon$ when $\Delta =3$.

Technically, this is achieved by leveraging the fractional local ratio technique, for a first application in a distributed setting.