On Centralized Smooth Scheduling

This paper studies evenly distributed sets of natural numbers and their applications to scheduling in a centralized environment. Such sets, called smooth sets, have the property that their quantity within each interval is proportional to the size of the interval, up to a bounded additive deviation; namely, for ρ,Δ∈ℝ a set A of natural numbers is (ρ,Δ)‐smooth if abs(|I|·ρ-|I∩A|)<Δ for any interval I⊂ℕ.