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Ad auctions in sponsored search support "broad match" that allows an advertiser to target a large number of queries while bidding only on a limited number. While giving more expressiveness to advertisers, this feature makes it challenging to optimize bids to maximize their returns: choosing to bid on a query as a broad match because it provides high profit results in one bidding for related queries which may yield low or even negative profits.

We abstract and study the complexity of the {\em bid optimization problem} which is to determine an advertiser's bids on a subset of keywords (possibly using broad match) so that her profit is maximized. In the query language model when the advertiser is allowed to bid on all queries as broad match, we present a linear programming (LP)-based polynomial-time algorithm that gets the optimal profit. In the model in which an advertiser can only bid on keywords, ie., a subset of …