A threshold of ln n for approximating set cover
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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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A combinatorial strongly polynomial algorithm for minimizing submodular functions
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On rectangle packing: maximizing benefits
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Tight approximation algorithms for maximum general assignment problems
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An improved approximation algorithm for combinatorial auctions with submodular bidders
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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
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Maximizing Non-Monotone Submodular Functions
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Tight information-theoretic lower bounds for welfare maximization in combinatorial auctions
Proceedings of the 9th ACM conference on Electronic commerce
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Inapproximability results for combinatorial auctions with submodular utility functions
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A note on maximizing a submodular set function subject to a knapsack constraint
Operations Research Letters
Tight information-theoretic lower bounds for welfare maximization in combinatorial auctions
Proceedings of the 9th ACM conference on Electronic commerce
Santa Claus Meets Hypergraph Matchings
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Approximating submodular functions everywhere
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Maximizing submodular set functions subject to multiple linear constraints
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Stochastic Submodular Maximization
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Non-monotone submodular maximization under matroid and knapsack constraints
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Truthful Mechanisms via Greedy Iterative Packing
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Submodular Maximization over Multiple Matroids via Generalized Exchange Properties
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Online Ad Assignment with Free Disposal
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Approximation Algorithms for Combinatorial Auctions with Complement-Free Bidders
Mathematics of Operations Research
Computation and incentives in combinatorial public projects
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Inapproximability for VCG-based combinatorial auctions
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Correlation robust stochastic optimization
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Thresholded covering algorithms for robust and max-min optimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Submodular Maximization over Multiple Matroids via Generalized Exchange Properties
Mathematics of Operations Research
Single-parameter combinatorial auctions with partially public valuations
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Constrained non-monotone submodular maximization: offline and secretary algorithms
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You share, i share: network effects and economic incentives in P2P file-sharing systems
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Maximizing Nonmonotone Submodular Functions under Matroid or Knapsack Constraints
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Approximability of combinatorial problems with multi-agent submodular cost functions
ACM SIGecom Exchanges
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Submodular function maximization via the multilinear relaxation and contention resolution schemes
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Word alignment via submodular maximization over matroids
HLT '11 Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies: short papers - Volume 2
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
Tight Approximation Algorithms for Maximum Separable Assignment Problems
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Black-box reductions in mechanism design
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SIAM Journal on Computing
Mechanism design via correlation gap
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Submodular maximization by simulated annealing
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Optimization with demand oracles
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ACM Transactions on Algorithms (TALG)
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Maximizing a Monotone Submodular Function Subject to a Matroid Constraint
SIAM Journal on Computing
Price of Correlations in Stochastic Optimization
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ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part II
Welfare maximization and the supermodular degree
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Annals of Mathematics and Artificial Intelligence
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In the Submodular Welfare Problem, m items are to be distributed among n players with utility functions wi: 2[m] → R+. The utility functions are assumed to be monotone and submodular. Assuming that player i receives a set of items Si, we wish to maximize the total utility ∑i=1n wi(Si). In this paper, we work in the value oracle model where the only access to the utility functions is through a black box returning wi(S) for a given set S. Submodular Welfare is in fact a special case of the more general problem of submodular maximization subject to a matroid constraint: max{f(S): S ∈ I}, where f is monotone submodular and I is the collection of independent sets in some matroid. For both problems, a greedy algorithm is known to yield a 1/2-approximation [21, 16]. In special cases where the matroid is uniform (I = S: |S| ≤ k) [20] or the submodular function is of a special type [4, 2], a (1-1/e)-approximation has been achieved and this is optimal for these problems in the value oracle model [22, 6, 15]. A (1-1/e)-approximation for the general Submodular Welfare Problem has been known only in a stronger demand oracle model [4], where in fact 1-1/e can be improved [9]. In this paper, we develop a randomized continuous greedy algorithm which achieves a (1-1/e)-approximation for the Submodular Welfare Problem in the value oracle model. We also show that the special case of n equal players is approximation resistant, in the sense that the optimal (1-1/e)-approximation is achieved by a uniformly random solution. Using the pipage rounding technique [1, 2], we obtain a (1-1/e)-approximation for submodular maximization subject to any matroid constraint. The continuous greedy algorithm has a potential of wider applicability, which we demonstrate on the examples of the Generalized Assignment Problem and the AdWords Assignment Problem.