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arXiv · 2009.04114

Adwords in a Panorama

Zhiyi Huang·Qiankun Zhang·Yuhao Zhang
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Abstract

Three decades ago, Karp, Vazirani, and Vazirani (STOC 1990) defined the online matching problem and gave an optimal $1-\frac{1}{e} \approx 0.632$-competitive algorithm. Fifteen years later, Mehta, Saberi, Vazirani, and Vazirani (FOCS 2005) introduced the first generalization called AdWords driven by online advertising and obtained the optimal $1-\frac{1}{e}$ competitive ratio in the special case of small bids. It has been open ever since whether there is an algorithm for general bids better than the $0.5$-competitive greedy algorithm. This paper presents a $0.5016$-competitive algorithm for AdWords, answering this open question on the positive end. The algorithm builds on several ingredients, including a combination of the online primal dual framework and the configuration linear program of matching problems recently explored by Huang and Zhang (STOC 2020), a novel formulation of AdWords which we call the panorama view, and a generalization of the online correlated selection by Fahrbach, Huang, Tao, and Zadimorghaddam (FOCS 2020) which we call the panoramic online correlated selection.

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Zhiyi Huang, Qiankun Zhang, Yuhao Zhang. 2020-11-27. Adwords in a Panorama. https://arxiv.org/abs/2009.04114

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