AdWords in a Panorama

Abstract

Three decades ago, Karp, Vazirani, and Vazirani (Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, 1990, pp. 352-358] defined the online matching problem and gave an optimal 1-0.632-competitive algorithm. Fifteen years later, Mehta et al. [J. ACM, 54 (2007), pp. 22:1-22:19] introduced the first generalization called AdWords driven by online adver- tising and obtained the optimal 1 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 [Proceedings of the 52nd ACM Symposium on Theory of Computing, 2020), a novel formulation of AdWords which we call the panorama view, and a generalization of the online correlated selection by Fahrbach et al. [Proceedings of the 61st Annual IEEE Symposium on Foundations of Computer Science, 2020], which we call the panoramic online correlated selection.