Three decades ago, Karp, Vazirani, and Vazirani (STOC 1990) defined the online matching problem and gave an optimal 1-1{e} \approx 0.632-competitive algorithm. \%introduced the Ranking algorithm with the optimal 1-\frac{1 Fifteen years later, Mehta, Saberi, Vazirani, and Vazirani (FOCS 2005) introduced the first generalization called AdWords driven by online advertising and obtained the optimal 1-1{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 URLhaddam (FOCS 2020) which we call the panoramic online correlated selection.
Three decades ago, Karp, Vazirani, and Vazirani (STOC 1990) defined the online matching problem and gave an optimal 1-1{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 1-1{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 URLhaddam (FOCS 2020) which we call the panoramic online correlated selection.
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\%introduced the Ranking algorithm with the optimal 1-\frac{1
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AdWords
AdWords
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small bids
small bids
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general bids
general bids