Distributed fractional local ratio and independent set approximation

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 poly(Δ,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 [Formula presented], and a further improvement to 8/5+ε when Δ=3. Technically, this is achieved by leveraging the fractional local ratio technique, for a first application in a distributed setting.