Pinwheel scheduling with three distinct numbers

Abstract

Given a multiset of positive integers A={a/sub 1/, a/sub 2/, ..., a/sub 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/sub i/. The density of A is defined as /spl rho/(A)=/spl Sigmasub i=1sup n/ (1/a/sub 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/spl ap/0.83 density threshold. This scheduler has achieved the exact theoretical bound of this problem.<>