Scheduling Multiprocessor Tasks with Equal Processing Times as a Mixed Graph Coloring Problem

This article extends the scheduling problem with dedicated processors, unit-time tasks, and minimizing maximal lateness Lmax for integer due dates to problem, where along precedence constraints given on set V={v1,v2, …,vn} of multiprocessor a subset tasks must be processed simultaneously. Contrary classical shop-scheduling several processors fulfill task. Furthermore, two types may task V. We prove that extended release times ri≥0 jobs V minimize schedule length Cmax solved as an optimal mixed graph coloring consists assignment minimal number colors (positive integers) {1,2, …,t} vertices {v1,v2, …,vn}=V G=(V,A, E) such that, if vp vq are joined by edge [vp,vq]∈E, their have different. Further, vi vj arc (vi,vj)∈A, color vertex has no greater than vj. theorems, which imply most analytical results proved so far colorings graphs E), analogous results, valid problems or lateness, vice versa.