Bidding and allocation in combinatorial auctions
Proceedings of the 2nd ACM conference on Electronic commerce
Combinatorial auctions with decreasing marginal utilities
Proceedings of the 3rd ACM conference on Electronic Commerce
Approximation algorithms for combinatorial auctions with complement-free bidders
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On the computational power of iterative auctions
Proceedings of the 6th ACM conference on Electronic commerce
An improved approximation algorithm for combinatorial auctions with submodular bidders
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On maximizing welfare when utility functions are subadditive
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Maximizing Non-Monotone Submodular Functions
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
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
Inapproximability results for combinatorial auctions with submodular utility functions
WINE'05 Proceedings of the First international conference on Internet and Network Economics
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
Optimizing query rewrites for keyword-based advertising
Proceedings of the 9th ACM conference on Electronic commerce
Non-monotone submodular maximization under matroid and knapsack constraints
Proceedings of the forty-first annual ACM symposium on Theory of computing
The Balloon Popping Problem Revisited: Lower and Upper Bounds
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Approximation Algorithms for Combinatorial Auctions with Complement-Free Bidders
Mathematics of Operations Research
Single-parameter combinatorial auctions with partially public valuations
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Maximizing Nonmonotone Submodular Functions under Matroid or Knapsack Constraints
SIAM Journal on Discrete Mathematics
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
Submodular function maximization via the multilinear relaxation and contention resolution schemes
Proceedings of the forty-third annual ACM symposium on Theory of computing
Optimal allocation in combinatorial auctions with quadratic utility functions
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
ESA'11 Proceedings of the 19th European conference on Algorithms
Maximizing Non-monotone Submodular Functions
SIAM Journal on Computing
Secondary spectrum auctions for symmetric and submodular bidders
Proceedings of the 13th ACM Conference on Electronic Commerce
Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
SIAM Journal on Computing
Approximation algorithms for online weighted rank function maximization under matroid constraints
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Combinatorial walrasian equilibrium
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Minimizing the total weighted completion time of fully parallel jobs with integer parallel units
Theoretical Computer Science
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We provide tight information-theoretic lower bounds for the welfare maximization problem in combinatorial auctions. In this problem, the goal is to partition m items among k bidders in a way that maximizes the sum of bidders' values for their allocated items. Bidders have complex preferences over items expressed by valuation functions that assign values to all subsets of items. We study the "black box" setting in which the auctioneer has oracle access to the valuation functions of the bidders. In particular, we explore the well-known value query model in which the permitted query to a valuation function is in the form of a subset of items, and the reply is the value assigned to that subset of items by the valuation function. We consider different classes of valuation functions: submodular,subadditive, and superadditive. For these classes, it has been shown that one can achieve approximation ratios of 1 -- 1/e, 1/√m, and √ m/m, respectively, via a polynomial (in k and m) number of value queries. We prove that these approximation factors are essentially the best possible: For any fixed ε 0, a (1--1/e + ε)-approximation for submodular valuations or an 1/m1/2-ε-approximation for subadditive valuations would require exponentially many value queries, and a log1+ε m/ m-approximation for superadditive valuations would require a superpolynomial number of value queries.