ABSTRACT
This chapter discusses the state-of-the-art, both in terms of approximation algorithms, lower bounds, and polynomial time solvability. It explores the problems, both from a scheduling and from a graph theory perspective, before setting the stage. The chapter considers two objective functions: minimizing the total length of the schedule and minimizing the average completion time. The resource-constrained scheduling problem can then be modeled as a multicoloring problem on the conflict graph. The jobs naturally define a conflict graph with vertices representing jobs, and with an edge between a pair of jobs that require the same resource. Graphs of small treewidth are a good example of graphs that can be handled efficiently, by efficient solution of p-bounded graphs and classical rounding-and-scaling.
