  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.
