The general adwords problem has remained largely unresolved. We define a subcase called {\em $k$-TYPICAL}, $k \in \Zplus$, as follows: the total budget of all the bidders is sufficient to buy $k$ bids for each bidder. This seems a reasonable assumption for a "typical" instance, at least for moderate values of $k$. We give a randomized online algorithm achieving a competitive ratio of $\left(1 - {1 \over e} - {1 \over k} \right) $ for this problem. We also give randomized online algorithms for other special cases of adwords. We give randomized online algorithms for other special cases of adwords as well, including an optimal algorithm for the case when the bids are small compared to budgets. This case captures a central computational issue that arises in the context of ad auctions, for instance in Google's AdWords marketplace. Previous algorithms for this case were deterministic \cite{MSVV, Buchbinder2007online} and were based on LP-duality. The key to these results is a simplification of the proof for RANKING, the optimal algorithm for online bipartite matching, given in \cite{KVV}. Our algorithms for adwords can be seen as natural extensions of RANKING.

翻译：一般广告问题基本上仍未解决。 我们定义了一个名为 $ $k$- TyPical}, $k $ $ $ +$ 的子案例, 具体如下: 所有投标人的总预算足以为每个投标人购买 $ 美元 标书。 这似乎是“ 典型” 实例的合理假设, 至少在中值 $k$。 我们给出了一个随机的在线算法, 其竞争性比率为$left(1 - {1\ over e} - {1\ over k} - {cited { MSV, Buchbinder2007 AN} 。 我们还为其他特殊广告案例提供随机化的在线算法。 我们给出了其他特殊标书的随机化在线算法, 包括当标书与预算相比小时的最佳算法。 这个案例记录了在拍卖过程中出现的中心计算问题, 例如在Google's AdWords 市场中。 这个案例的前算法是确定性 { MSV, Buchbinder2007 AN} 并基于 IMK privalalalalalalalal_ practalalalal_ 。 。 view dalalalal_ 。 。 将这些关键算法作为我们的精准的精准的精准。