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The design of revenue-maximizing combinatorial auctions, i.e. multi-item auctions over bundles of goods, is one of the most fundamental problems in computational economics, unsolved even for two bidders and two items for sale. In the traditional economic models, it is assumed that the bidders' valuations are drawn from an underlying distribution and that(More)
A large body of work in machine learning has focused on the problem of learning a close approximation to an underlying combinatorial function, given a small set of labeled examples. However, for real-valued functions, cardinal labels might not be accessible, or it may be difficult for an expert to consistently assign real-valued labels over the entire set(More)
D. Schattschneider proved that there are exactly eight unilateral and equitransitive tilings of the plane by squares of three distinct sizes. This article extends Schattschneider's methods to determine a classification of all such tilings by squares of four different sizes. It is determined that there are exactly 39 unilateral and equitransitive tilings by(More)
We study the design of pricing mechanisms and auctions when the mechanism designer does not know the distribution of buyers’ values. Instead the mechanism designer receives a set of samples from this distribution and his goal is to use the sample to design a pricing mechanism or auction with high expected profit. We provide generalization guarantees which(More)
Many data analysis problems are NP-hard, a reality that has motivated researchers to develop a wealth of approximation algorithms and heuristics over the past few decades. Max-cut, clustering, and many other partitioning problems fall into this camp, with widespread applications ranging from statistical physics to computational biology. In this work, we(More)
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