A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
The budgeted maximum coverage problem
Information Processing Letters
Combinatorial auctions with decreasing marginal utilities
Proceedings of the 3rd ACM conference on Electronic Commerce
Incentive compatible multi unit combinatorial auctions
Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge
Approximation algorithms for combinatorial auctions with complement-free bidders
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Exponential communication inefficiency of demand queries
TARK '05 Proceedings of the 10th conference on Theoretical aspects of rationality and knowledge
Truthful and Near-Optimal Mechanism Design via Linear Programming
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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
Truthful randomized mechanisms for combinatorial auctions
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
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
Item pricing for revenue maximization
Proceedings of the 9th ACM conference on Electronic commerce
Maximizing submodular set functions subject to multiple linear constraints
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Non-monotone submodular maximization under matroid and knapsack constraints
Proceedings of the forty-first annual ACM symposium on Theory of computing
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
On the Computational Power of Demand Queries
SIAM Journal on Computing
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Mechanisms for complement-free procurement
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
Submodular function maximization via the multilinear relaxation and contention resolution schemes
Proceedings of the forty-third annual ACM symposium on Theory of computing
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Inapproximability results for combinatorial auctions with submodular utility functions
WINE'05 Proceedings of the First international conference on Internet and Network Economics
On the approximability of budget feasible mechanisms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Submodular maximization by simulated annealing
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A note on maximizing a submodular set function subject to a knapsack constraint
Operations Research Letters
Combinatorial walrasian equilibrium
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We study combinatorial procurement auctions, where a buyer with a valuation function v and budget B wishes to buy a set of items. Each item i has a cost ci and the buyer is interested in a set S that maximizes v(S) subject to ∑i∈Sci ≤ β. Special cases of combinatorial procurement auctions are well-studied problems from submodular optimization. In particular, when the costs are all equal (cardinality constraint), a classic result by Nemhauser et al shows that the greedy algorithm provides an e/e-1 approximation. Motivated by many papers that utilize demand queries to elicit the preferences of agents in economic settings, we develop algorithms that guarantee improved approximation ratios in the presence of demand oracles. We are able to break the e/e-1 barrier: we present algorithms that use only polynomially many demand queries and have approximation ratios of 9/8+∈ for the general problem and 9/8 for maximization subject to a cardinality constraint. We also consider the more general class of subadditive valuations. We present algorithms that obtain an approximation ratio of 2+∈ for the general problem and 2 for maximization subject to a cardinality constraint. We guarantee these approximation ratios even when the valuations are non-monotone. We show that these ratios are essentially optimal, in the sense that for any constant ∈0, obtaining an approximation ratio of 2-∈ requires exponentially many demand queries.