Lagrangian Duality in Online Scheduling with Resource Augmentation and Speed Scaling

Abstract : We present an unified approach to study online scheduling problems in the resource augmentation/speed scaling models. Potential function method is extensively used for analyzing algorithms in these models; however, they yields little insight on how to construct potential functions and how to design algorithms for related problems. In the paper, we generalize and strengthen the dual-fitting technique proposed by Anand et al. [1]. The approach consists of considering a possibly non-convex relaxation and its Lagrangian dual; then constructing dual variables such that the Lagrangian dual has objective value within a desired factor of the primal optimum. The competitive ratio follows by the standard Lagrangian weak duality. This approach is simple yet powerful and it is seemingly a right tool to study problems with resource augmentation or speed scaling. We illustrate the approach through the following results.
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Kim Thang Nguyen. Lagrangian Duality in Online Scheduling with Resource Augmentation and Speed Scaling. 21st European Symposium on Algorithms (ESA 2013), Sep 2013, Sophia Antipolis, France. pp.755--766, ⟨10.1007/978-3-642-40450-4_64⟩. ⟨hal-00867456⟩

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