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Motivated by recent insights into the online bipartite matching problem(\textsc{OBM}), our goal was to extend the optimal algorithm for it, namely\textsc{Ranking}, all the way to the special case of adwords problem, called\textsc{Small}, in which bids are small compared to budgets; the latter hasbeen of considerable practical significance in ad auctions \cite{MSVV}. Theattractive feature of our approach was that it would yield a {\embudget-oblivious algorithm}, i.e., the algorithm would not need to know budgetsof advertisers and therefore could be used in autobidding platforms.  We were successful in obtaining an optimal, budget-oblivious algorithm for\textsc{Single-Valued}, under which each advertiser can make bids of one valueonly. However, our next extension, to \textsc{Small}, failed because of afundamental reason, namely failure of the {\em No-Surpassing Property}. Sincethe probabilistic ideas underlying our algorithm are quite substantial, we havestated them formally, after assuming the No-Surpassing Property, and we leavethe open problem of removing this assumption.  With the help of two undergrads, we conducted extensive experiments on ouralgorithm on randomly generated instances. Our findings are that theNo-Surpassing Property fails less than $2\%$ of the time and that theperformance of our algorithms for \textsc{Single-Valued} and \textsc{Small} arecomparable to that of \cite{MSVV}. If further experiments confirm this, ouralgorithm may be useful as such in practice, especially because of itsbudget-obliviousness.

Towards a Practical, Budget-Oblivious Algorithm for the Adwords Problem under Small Bids