Indential parallel machines vs. unit-time shops and preemptions vs. chains in scheduling complexity

This paper surveys, analyses and establishes new polynomial-time reductions among scheduling problems that connect identical parallel machines with unit-time shops and the preemption facility with chain-like precedence constraints in same machine environments. The reductions turn out to be unexpectedly fruitful in clarifying the complexity status of many scheduling problems that were open before. The main purpose of this paper is revealing the relationship between problems in different scheduling classes.