Extending LOCAL lower bounds beyond LOCAL to quantum-LOCAL and bounded-dependence models

Ascertain whether locality lower bounds for minimum dominating set analogous to those established in the LOCAL model also hold in stronger distributed models, including quantum-LOCAL and bounded-dependence, for comparable approximation ratios and on n-vertex graphs with maximum degree Δ.

Background

Beyond the LOCAL model, modern distributed settings include quantum-LOCAL and bounded-dependence models. While some degree-dependent lower bounds are known to extend to quantum-LOCAL, the status of Ω(log n)-scale bounds even for constant factors has remained unclear in these stronger models.

The authors explicitly identify the question of transferring such locality lower bounds beyond LOCAL as one of two central open problems motivating their work.