Lagrangian Primal Dual Algorithms in Online Scheduling

We present a primal-dual approach to design algorithms in online scheduling. Our approach makes use of the Lagrangian weak duality and convexity to derive dual programs for problems which could be formulated as convex assignment problems. The constraints of the duals explicitly indicate the online decisions and naturally lead to competitive algorithms. We illustrate the advantages and the flexibility of the approach through problems in different setting: from single machine to unrelated machine environments, from typical competitive analysis to the one with resource augmentation, from convex relaxations to non-convex relaxations.