Section: New Results
Online Non-preemptive Scheduling in a Resource Augmentation Model based on Duality
Resource augmentation is a well-established model for analyzing algorithms, particularly in the
online setting. It has been successfully used for providing theoretical evidence for several heuristics
in scheduling with good performance in practice. According to this model, the algorithm is
applied to a more powerful environment than that of the adversary. Several types of resource
augmentation for scheduling problems have been proposed up to now, including speed augmentation,
machine augmentation and more recently rejection. In this paper [7], we present a framework
that unifies the various types of resource augmentation. Moreover, it allows generalize the notion
of resource augmentation for other types of resources. Our framework is based on mathematical
programming and it consists of extending the domain of feasible solutions for the algorithm with
respect to the domain of the adversary. This, in turn allows the natural concept of duality for
mathematical programming to be used as a tool for the analysis of the algorithm’s performance.
As an illustration of the above ideas, we apply this framework and we propose a primal-dual
algorithm for the online scheduling problem of minimizing the total weighted flow time of jobs on
unrelated machines when the preemption of jobs is not allowed. This is a well representative problem
for which no online algorithm with performance guarantee is known. Specifically, a strong
lower bound of