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26
Adwords and generalized online matching
 In FOCS ’05: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
, 2005
"... How does a search engine company decide what ads to display with each query so as to maximize its revenue? This turns out to be a generalization of the online bipartite matching problem. We introduce the notion of a tradeoff revealing LP and use it to derive two optimal algorithms achieving competit ..."
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Cited by 106 (5 self)
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How does a search engine company decide what ads to display with each query so as to maximize its revenue? This turns out to be a generalization of the online bipartite matching problem. We introduce the notion of a tradeoff revealing LP and use it to derive two optimal algorithms achieving competitive ratios of 1 − 1/e for this problem. 1
Approximation algorithms for combinatorial auctions with complementfree bidders
 In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC
, 2005
"... We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items m and in the number of bidders n, even though the “input size ” is exponential in m. The first algori ..."
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Cited by 104 (22 self)
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We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items m and in the number of bidders n, even though the “input size ” is exponential in m. The first algorithm provides an O(log m) approximation. The second algorithm provides an O ( √ m) approximation in the weaker model of value oracles. This algorithm is also incentive compatible. The third algorithm provides an improved 2approximation for the more restricted case of “XOS bidders”, a class which strictly contains submodular bidders. We also prove lower bounds on the possible approximations achievable for these classes of bidders. These bounds are not tight and we leave the gaps as open problems. 1
The adwords problem: Online keyword matching with budgeted bidders under random permutations
 In Proc. 10th Annual ACM Conference on Electronic Commerge (EC
, 2009
"... We consider the problem of a search engine trying to assign a sequence of search keywords to a set of competing bidders, each with a daily spending limit. The goal is to maximize the revenue generated by these keyword sales, bearing in mind that, as some bidders may eventually exceed their budget, n ..."
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Cited by 41 (4 self)
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We consider the problem of a search engine trying to assign a sequence of search keywords to a set of competing bidders, each with a daily spending limit. The goal is to maximize the revenue generated by these keyword sales, bearing in mind that, as some bidders may eventually exceed their budget, not all keywords should be sold to the highest bidder. We assume that the sequence of keywords (or equivalently, of bids) is revealed online. Our concern will be the competitive ratio for this problem versus the offline optimum. We extend the current literature on this problem by considering the setting where the keywords arrive in a random order. In this setting we are able to achieve a competitive ratio of 1 − ɛ under some mild, but necessary, assumptions.
Multiunit auctions with budget limits
 In Proc. of the 49th Annual Symposium on Foundations of Computer Science (FOCS
, 2008
"... We study multiunit auctions where the bidders have a budget constraint, a situation very common in practice that has received very little attention in the auction theory literature. Our main result is an impossibility: there are no incentivecompatible auctions that always produce a Paretooptimal ..."
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Cited by 38 (5 self)
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We study multiunit auctions where the bidders have a budget constraint, a situation very common in practice that has received very little attention in the auction theory literature. Our main result is an impossibility: there are no incentivecompatible auctions that always produce a Paretooptimal allocation. We also obtain some surprising positive results for certain special cases. 1
Online bipartite matching with unknown distributions
 In STOC
, 2011
"... We consider the online bipartite matching problem in the unknown distribution input model. We show that the Ranking algorithm of [KVV90] achieves a competitive ratio of at least 0.653. This is the first analysis to show an algorithm which breaks the natural 1 − 1/e ‘barrier ’ in the unknown distribu ..."
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Cited by 21 (1 self)
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We consider the online bipartite matching problem in the unknown distribution input model. We show that the Ranking algorithm of [KVV90] achieves a competitive ratio of at least 0.653. This is the first analysis to show an algorithm which breaks the natural 1 − 1/e ‘barrier ’ in the unknown distribution model (our analysis in fact works in the stricter, random order model) and answers an open question in [GM08]. We also describe a family of graphs on which Ranking does no better than 0.727 in the random order model. Finally, we show that for graphs which have k> 1 disjoint perfect matchings, Ranking achieves a competitive ratio of at least 1 −
Characterizing truthful multiarmed bandit mechanisms
 In ACMEC
, 2009
"... We consider a multiround auction setting motivated by payperclick auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. I ..."
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Cited by 15 (0 self)
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We consider a multiround auction setting motivated by payperclick auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. Initially, neither the auctioneer nor the advertisers have any information about the likelihood of clicks on the advertisements. The auctioneer’s goal is to design a (dominant strategies) truthful mechanism that (approximately) maximizes the social welfare. If the advertisers bid their true private values, our problem is equivalent to the multiarmed bandit problem, and thus can be viewed as a strategic version of the latter. In particular, for both problems the quality of an algorithm can be characterized by regret, the difference in social welfare between the algorithm and the benchmark which always selects the same“best”advertisement. We investigate how the design of multiarmed bandit algorithms is affected by the restriction that the resulting mechanism must be truthful. We find that truthful mechanisms have certain strong structural properties – essentially, they must separate exploration from exploitation – and they incur much higher regret than the optimal multiarmed bandit algorithms. Moreover, we provide a truthful mechanism which (essentially) matches our lower bound on regret.
Optimal Online Assignment with Forecasts
"... We study a class of online assignment problems that naturally generalizes problems such as online bipartite matching, allocation, and budgeted bidders, in which we wish to minimize the value of some convex objective function subject to a set of linear supply and demand constraints. Motivated by real ..."
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Cited by 10 (1 self)
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We study a class of online assignment problems that naturally generalizes problems such as online bipartite matching, allocation, and budgeted bidders, in which we wish to minimize the value of some convex objective function subject to a set of linear supply and demand constraints. Motivated by real world conditions where the online input is often far from worstcase, we formulate the online assignment with forecast problem. In this model, we assume to have access to random samples from the future set of arriving vertices. We propose a novel use of the dual space for convex optimization problems. By working in the subspace of the dual space, we are able to describe the optimal primal solution implicitly in space proportional to the demand side of the input graph. More importantly, we prove that representing the primal solution using such a compact allocation plan yields a robust online algorithm which is able to make nearoptimal online decisions, generalizing the solution even to unsampled (and previously unseen) input.
Selling banner ads: Online algorithms with buyback
 In Fourth Workshop on Ad Auctions
, 2008
"... We initiate the study of online pricing problems in markets with “buyback, ” i.e., markets in which prior allocation decisions can be revoked, but at a cost. In our model, a seller receives requests online and chooses which requests to accept, subject to constraints on the subsets of requests which ..."
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Cited by 9 (0 self)
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We initiate the study of online pricing problems in markets with “buyback, ” i.e., markets in which prior allocation decisions can be revoked, but at a cost. In our model, a seller receives requests online and chooses which requests to accept, subject to constraints on the subsets of requests which may be accepted simultaneously. A request, once accepted, can be canceled at a cost which is a fixed fraction of the request value. This scenario models a market for web advertising, in which the buyback cost represents the cost of canceling an existing contract. We analyze a simple constantcompetitive algorithm for a singleitem auction in this model, and we prove that its competitive ratio is optimal among deterministic algorithms. Moreover, we prove that an extension of this algorithm achieves the same competitive ratio in any matroid domain, i.e., when the sets of requests which may be simultaneously satisfied constitute the independent sets of a matroid. This broad class of domains includes, for example, advertising markets in which each request is for a unit of supply coming from a specified subset of the available impressions. We also present algorithms and lower bounds for knapsack domains, i.e., when advertisers request varying quantities of a homogeneous but limited supply of impressions. 1.
Secretary Problems via Linear Programming
"... Abstract. In the classical secretary problem an employer would like to choose the best candidate among n competing candidates that arrive in a random order. This basic concept of n elements arriving in a random order and irrevocable decisions made by an algorithm have been explored extensively over ..."
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Abstract. In the classical secretary problem an employer would like to choose the best candidate among n competing candidates that arrive in a random order. This basic concept of n elements arriving in a random order and irrevocable decisions made by an algorithm have been explored extensively over the years, and used for modeling the behavior of many processes. Our main contribution is a new linear programming technique that we introduce as a tool for obtaining and analyzing mechanisms for the secretary problem and its variants. The linear program is formulated using judiciously chosen variables and constraints and we show a onetoone correspondence between mechanisms for the secretary problem and feasible solutions to the linear program. Capturing the set of mechanisms as a linear polytope holds the following immediate advantages. – Computing the optimal mechanism reduces to solving a linear program. – Proving an upper bound on the performance of any mechanism reduces to finding a feasible solution to the dual program. – Exploring variants of the problem is as simple as adding new constraints, or manipulating the objective function of the linear program. We demonstrate these ideas by exploring some natural variants of the secretary problem. In particular, using our approach, we design optimal secretary mechanisms in which the probability of selecting a candidate at any position is equal. We refer to such mechanisms as incentive compatible and these mechanisms are motivated by the recent applications of secretary problems to online auctions. We also show a family of linear programs which characterize all mechanisms that are allowed to choose J candidates and gain profit from the K best candidates. We believe that linear programming based approach may be very helpful in the context of other variants of the secretary problem. 1