
LPbased Approximation for Personalized Reserve Prices
We study the problem of computing revenueoptimal personalize (nonanony...
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Total Domination in Unit Disk Graphs
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Escaping Cannibalization? CorrelationRobust Pricing for a UnitDemand Buyer
A single seller wishes to sell n items to a single unitdemand buyer. We...
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Hierarchical Clustering: a 0.585 Revenue Approximation
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Approximation Algorithms for Coordinating Ad Campaigns on Social Networks
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Beating Greedy For Approximating Reserve Prices in MultiUnit VCG Auctions
We study the problem of finding personalized reserve prices for unitdemand buyers in multiunit eager VCG auctions with correlated buyers. The input to this problem is a dataset of submitted bids of n buyers in a set of auctions. The goal is to find a vector of reserve prices, one for each buyer, that maximizes the total revenue across all auctions. Roughgarden and Wang (2016) showed that this problem is APXhard but admits a greedy 1/2approximation algorithm. Later, Derakhshan, Golrezai, and Paes Leme (2019) gave an LPbased algorithm achieving a 0.68approximation for the (important) special case of the problem with a singleitem, thereby beating greedy. We show in this paper that the algorithm of Derakhshan et al. in fact does not beat greedy for the general multiitem problem. This raises the question of whether or not the general problem admits a betterthan1/2 approximation. In this paper, we answer this question in the affirmative and provide a polynomialtime algorithm with a significantly better approximationfactor of 0.63. Our solution is based on a novel linear programming formulation, for which we propose two different rounding schemes. We prove that the best of these two and the noreserve case (allzero vector) is a 0.63approximation.
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