Primal-Dual and Dual-Fitting Analysis of Online Scheduling Algorithms for Generalized Flow Time Problems

We study a variety of online scheduling problems on a single processor that can be viewed as extensions of the well-studied problem of minimizing total weighted flow time. Most previous work on this class of problems has relied on amortized analysis and the use of complicated potential-function arguments. In this paper we follow a different approach based on the primal-dual and dual-fitting paradigms. In particular, we provide a framework of analysis that is derived by duality properties, does not rely on potential functions, gives insights for new algorithms, and is applicable to a variety of scheduling problems. We begin with an interpretation of the algorithm Highest-Density-First (HDF) as a primal-dual algorithm, and a corresponding proof that HDF is optimal for total weighted fractional flow time, which directly implies that it is scalable for the integral objective. Building upon the salient ideas of the proof, we show how to apply and extend this analysis to the more general problem of minimizing the objective