Characterization of the Critical Posets in Two-Machine Unit Time Scheduling

Summary

Scheduling of partially ordered unit time jobs on m machines, aiming at minimal schedule length, is known as one of the notorious combinatorial optimization problems, for which the complexity status still is unresolved. Available results give polynomial time algorithms for special classes of partial orders and for the case m = 2. From a systematicial point of view, insight into the minimal (critical) posets with a certain optimal schedule length could be pivotal for finding polynomial time algorithms in general. The paper includes some comments on this approach, the complete characterization of the minimal posets in case m = 2 and some remarks on minimal posets in case m > 2.