TY - GEN
T1 - Online Ad assignment with free disposal
AU - Feldman, Jon
AU - Korula, Nitish
AU - Mirrokni, Vahab
AU - Muthukrishnan, S.
AU - Pál, Martin
PY - 2009
Y1 - 2009
N2 - We study an online weighted assignment problem with a set of fixed nodes corresponding to advertisers and online arrival of nodes corresponding to ad impressions. Advertiser a has a contract for n(a) impressions, and each impression has a set of weighted edges to advertisers. The problem is to assign the impressions online so that while each advertiser a gets n(a) impressions, the total weight of edges assigned is maximized. Our insight is that ad impressions allow for free disposal, that is, advertisers are indifferent to, or prefer being assigned more than n(a) impressions without changing the contract terms. This means that the value of an assignment only includes the n(a) highest-weighted items assigned to each node a. With free disposal, we provide an algorithm for this problem that achieves a competitive ratio of 1-1/e against the offline optimum, and show that this is the best possible ratio. We use a primal/dual framework to derive our results, applying a novel exponentially-weighted dual update rule. Furthermore, our algorithm can be applied to a general set of assignment problems including the ad words problem as a special case, matching the previously known 1-1/e competitive ratio.
AB - We study an online weighted assignment problem with a set of fixed nodes corresponding to advertisers and online arrival of nodes corresponding to ad impressions. Advertiser a has a contract for n(a) impressions, and each impression has a set of weighted edges to advertisers. The problem is to assign the impressions online so that while each advertiser a gets n(a) impressions, the total weight of edges assigned is maximized. Our insight is that ad impressions allow for free disposal, that is, advertisers are indifferent to, or prefer being assigned more than n(a) impressions without changing the contract terms. This means that the value of an assignment only includes the n(a) highest-weighted items assigned to each node a. With free disposal, we provide an algorithm for this problem that achieves a competitive ratio of 1-1/e against the offline optimum, and show that this is the best possible ratio. We use a primal/dual framework to derive our results, applying a novel exponentially-weighted dual update rule. Furthermore, our algorithm can be applied to a general set of assignment problems including the ad words problem as a special case, matching the previously known 1-1/e competitive ratio.
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U2 - 10.1007/978-3-642-10841-9_34
DO - 10.1007/978-3-642-10841-9_34
M3 - Conference contribution
AN - SCOPUS:76749168646
SN - 3642108407
SN - 9783642108402
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 374
EP - 385
BT - Internet and Network Economics - 5th International Workshop, WINE 2009, Proceedings
T2 - 5th International Workshop on Internet and Network Economics, WINE 2009
Y2 - 14 December 2009 through 18 December 2009
ER -