Budget Optimization in Search-Based Advertising Auctions
  Internet search companies sell advertisement slots based on users' search queries via an auction. While there has been a lot of attention on the auction process and its game-theoretic aspects, our focus is on the advertisers. In particular, the advertisers have to solve a complex optimization problem of how to place bids on the keywords of their interest so that they can maximize their return (the number of user clicks on their ads) for a given budget. We model the entire process and study this budget optimization problem. While most variants are NP hard, we show, perhaps surprisingly, that simply randomizing between two uniform strategies that bid equally on all the keywords works well. More precisely, this strategy gets at least 1-1/e fraction of the maximum clicks possible. Such uniform strategies are likely to be practical. We also present inapproximability results, and optimal algorithms for variants of the budget optimization problem. 
Jon Feldman, S. Muthukrishnan, Martin Pal, Cliff Stein