You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: A survey on how the structure of precedence constraints may change the complexity class of scheduling problems 
Chapter Title:  11 
1. Abstract of Cited Paper (BIB001):  The problem of minimizing the total tardiness for a set of unit-processing-time jobs on a single machine is considered. J. K. Lenstra and A. H. G. Rinnooy Kan have shown that the problem is NP-hard if the jobs have arbitrary precedence constraints. They asked whether the problem remains NP-hard for tree-structured precedence constraints. In this paper we show that the problem is NP-hard even for a set of chains. Our result gives a sharp boundary for the complexity of this problem, since there is a simple, polynomial-time algorithm for a set of independent jobs. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Literature Review:
4 Single machine problems For single machine problems, most of the interesting results for this survey are related to the total weighted completion time w j C j . It is mainly due to the fact that 1|chains, p j = 1| U j (see BIB001 ) and 1|chains, p j = 1| T j (see BIB002 ) are already N P-hard, while 1|prec, r j |Cmax is solvable in polynomial time. Nevertheless, as we will see in Section 4.3, there are some interesting open problems for other criteria when considering preemption.