A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Combinatorial auctions with decreasing marginal utilities
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Approximation algorithms for combinatorial auctions with complement-free bidders
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Truthful and Near-Optimal Mechanism Design via Linear Programming
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Limitations of VCG-based mechanisms
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Optimal approximation for the submodular welfare problem in the value oracle model
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Soft Decoding, Dual BCH Codes, and Better List-Decodable e-Biased Codes
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Two Randomized Mechanisms for Combinatorial Auctions
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
On the Hardness of Being Truthful
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
On the Power of Randomization in Algorithmic Mechanism Design
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Computation and incentives in combinatorial public projects
Proceedings of the 11th ACM conference on Electronic commerce
Inapproximability for VCG-based combinatorial auctions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A truthful randomized mechanism for combinatorial public projects via convex optimization
Proceedings of the 12th ACM conference on Electronic commerce
An impossibility result for truthful combinatorial auctions with submodular valuations
Proceedings of the forty-third annual ACM symposium on Theory of computing
From convex optimization to randomized mechanisms: toward optimal combinatorial auctions
Proceedings of the forty-third annual ACM symposium on Theory of computing
Limitations of Randomized Mechanisms for Combinatorial Auctions
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Inapproximability results for combinatorial auctions with submodular utility functions
WINE'05 Proceedings of the First international conference on Internet and Network Economics
From query complexity to computational complexity
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Truthful mechanism design for multidimensional covering problems
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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One of the fundamental questions of Algorithmic Mechanism Design is whether there exists an inherent clash between truthfulness and computational tractability: in particular, whether polynomial-time truthful mechanisms for combinatorial auctions are provably weaker in terms of approximation ratio than non-truthful ones. This question was very recently answered for universally truthful mechanisms for combinatorial auctions [4], and even for truthful-in-expectation mechanisms [12]. However, both of these results are based on information-theoretic arguments for valuations given by a value oracle, and leave open the possibility of polynomial-time truthful mechanisms for succinctly described classes of valuations. This paper is the first to prove computational hardness results for truthful mechanisms for combinatorial auctions with succinctly described valuations. We prove that there is a class of succinctly represented submodular valuations for which no deterministic truthful mechanism provides an m1/2-∈-approximation for a constant ∈0, unless NP=RP (m denotes the number of items). Furthermore, we prove that even truthful-in-expectation mechanisms cannot approximate combinatorial auctions with certain succinctly described submodular valuations better than within nγ, where n is the number of bidders and γ0 some absolute constant, unless NP ⊆ P/poly. In addition, we prove computational hardness results for two related problems.