Pinwheel scheduling with three distinct numbers

Given a multiset of positive integers A={a₁, a₂ , ..., a_n}, the pinwheel problem is to find an infinite sequence over { 1, 2,..., n} such that there is at least one symbol i within any subsequence of length a_i. The density of A is defined as ρ(A)=Σ_i=1ⁿ (1/a_i). We limit ourselves to instances composed of three distinct integers. Currently, the best scheduler can schedule such instances with a density less than 0.77. A new and fast scheduling scheme based on spectrum partitioning is proposed which improves the 0.77 result to a new 5/6≈0.83 density threshold. This scheduler has achieved the exact theoretical bound of this problem