AdWords in a Panorama
Zhiyi Huang, Qiankun Zhang, Yuhao Zhang · SIAM Journal on Computing · 2020
Abstract. Three decades ago, Karp, Vazirani, and Vazirani [ Proceedings of the 22 nd Annual ACM Symposium on Theory of Computing, 1990, pp. 352–358] defined the online matching problem and gave an optimal [Formula: see text]-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 advertising and obtained the optimal [Formula: see text] 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 52 nd 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 61 st Annual IEEE Symposium on Foundations of Computer Science, 2020], which we call the panoramic online correlated selection.