Data structures and network algorithms
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Some optimal inapproximability results
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A threshold of ln n for approximating set cover
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Computationally feasible VCG mechanisms
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A combinatorial algorithm minimizing submodular functions in strongly polynomial time
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Combinatorial auctions with decreasing marginal utilities
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Algorithm for optimal winner determination in combinatorial auctions
Artificial Intelligence
Algorithmic derandomization via complexity theory
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Truth revelation in approximately efficient combinatorial auctions
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An approximate truthful mechanism for combinatorial auctions with single parameter agents
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Truthful randomized mechanisms for combinatorial auctions
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Algorithms for Recognizing Economic Properties in Matrix Bid Combinatorial Auctions
INFORMS Journal on Computing
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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 2-approximation 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.