Algorithms for Chromatic Sums, Multicoloring, and Scheduling Dependent Jobs

This survey deals with problems at the intersection of two scientific fields: graph theory and scheduling. They can either be viewed as scheduling dependent jobs – jobs with resource conflicts – or as graph coloring optimization involving different objective functions. Our main aim is to illustrate the various interesting algorithmic techniques that have been brought to bear. We will also survey the state of the art, both in terms of approximation algorithms, lower bounds, and polynomial time solvability. We first formulate the problems, both from a scheduling and from a graph theory perspective, before setting the stage.