Randomized Online Algorithms for Adwords

Vijay V. Vazirani

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. 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.

Knowledge Graph

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