Online Graph Algorithms with Predictions
Online Graph Algorithms with Predictions
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DOI：
10.1137/1.9781611977073.3
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
Y. Azar;Debmalya Panigrahi;Noam Touitou
中科院分区：
文献类型：
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作者：
Y. Azar;Debmalya Panigrahi;Noam Touitou
具有预测的在线算法是一个流行而优雅的框架，用于绕过竞争分析中的悲观下限。在此模型中，在线算法提供了未来的预测，其目标是竞争比率可以在预测错误的函数中平稳地插入最佳离线和在线界限。在本文中，我们研究了与预测有关的在线图形问题。我们的贡献如下： *第一个问题是定义预测错误。对于图/度量问题，可以存在两种类型的错误，未预测的位置，并且可以预测的位置，但是预测的位置和实际位置并不能完全重合。我们设计了一个对预测错误的新颖定义，称为度量错误，并与异常值同时捕获两种类型的错误，从而概括了以前的错误定义，该定义仅捕获两种错误类型之一。 *我们提供了一个通用框架，用于在某些技术条件下以“黑匣子”方式（现有在线和离线算法）结合在线算法。据我们所知，这是第一个通用工具，用于获取具有预测的在线算法。 *使用我们的框架，我们获得了几个经典图形问题的竞争比率的紧密界限，这是指标误差与异常值的函数：Steiner Tree，Steiner Forest，Priority Steiner Tree Tree/Forest以及未PACT的/无能力/电容的设施位置。与异常值的度量错误的定义以及将离线和在线算法组合的一般框架并不是我们本文中考虑的问题的特定特定的。我们希望这些对这个领域的未来工作有用。
Online algorithms with predictions is a popular and elegant framework for bypassing pessimistic lower bounds in competitive analysis. In this model, online algorithms are supplied with future predictions, and the goal is for the competitive ratio to smoothly interpolate between the best offline and online bounds as a function of the prediction error. In this paper, we study online graph problems with predictions. Our contributions are the following: * The first question is defining prediction error. For graph/metric problems, there can be two types of error, locations that are not predicted, and locations that are predicted but the predicted and actual locations do not coincide exactly. We design a novel definition of prediction error called metric error with outliers to simultaneously capture both types of errors, which thereby generalizes previous definitions of error that only capture one of the two error types. * We give a general framework for obtaining online algorithms with predictions that combines, in a"black box"fashion, existing online and offline algorithms, under certain technical conditions. To the best of our knowledge, this is the first general-purpose tool for obtaining online algorithms with predictions. * Using our framework, we obtain tight bounds on the competitive ratio of several classical graph problems as a function of metric error with outliers: Steiner tree, Steiner forest, priority Steiner tree/forest, and uncapacitated/capacitated facility location. Both the definition of metric error with outliers and the general framework for combining offline and online algorithms are not specific to the problems that we consider in this paper. We hope that these will be useful for future work in this domain.