基于Lagrangian对偶的在线调度算法
Lagrangian Duality based Algorithms in Online Scheduling
摘要：
我们认为拉格朗日对偶为基础的方法来设计和分析在线节能调度算法。首先，我们提出了一个原始对偶框架。我们的方法利用拉格朗日弱对偶性和凸性来导出对偶规划，这些对偶规划可以被表述为凸分配问题。该算法具有与线性规划一样的直观结构。的约束条件明确指出在线决策，并自然导致竞争的算法。其次，我们使用一个双重拟合的方法，这也是基于弱对偶，研究问题，不太可能承认凸松弛。通过分析，我们显示了一个有趣的功能，其中原始-对偶给出了设计算法的想法，而分析是通过对偶拟合完成的。我们通过不同环境下的问题来说明这些方法的优点和灵活性：从单机到不相关的机器环境，从典型的竞争分析到资源增加的分析，从凸松弛到非凸松弛。
英文摘要：
We consider Lagrangian duality based approaches to design and analyze algorithms for online energy-efficient scheduling. First, we present a primal-dual framework. 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 duals have intuitive structures as the ones in linear programming. The constraints of the duals explicitly indicate the online decisions and naturally lead to competitive algorithms. Second, we use a dual-fitting approach, which also based on the weak duality, to study problems which are unlikely to admit convex relaxations. Through the analysis, we show an interesting feature in which primal-dual gives idea for designing algorithms while the analysis is done by dual-fitting. We illustrate the advantages and the flexibility of the approaches 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.
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