An O(EV log V) algorithm for finding a maximal weighted matching in general graphs
SIAM Journal on Computing
The hardness of approximation: gap location
Computational Complexity
A d/2 approximation for maximum weight independent set in d-claw free graphs
Nordic Journal of Computing
Implementation of algorithms for maximum matching on nonbipartite graphs.
Implementation of algorithms for maximum matching on nonbipartite graphs.
An improved approximation algorithm for combinatorial auctions with submodular bidders
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the complexity of approximating k-set packing
Computational Complexity
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
Combinatorial auctions with k-wise dependent valuations
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
On Maximizing Welfare When Utility Functions Are Subadditive
SIAM Journal on Computing
Approximation Algorithms for Combinatorial Auctions with Complement-Free Bidders
Mathematics of Operations Research
On the Computational Power of Demand Queries
SIAM Journal on Computing
Combinatorial auctions with restricted complements
Proceedings of the 13th ACM Conference on Electronic Commerce
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Given a set of items and a collection of players, each with a nonnegative monotone valuation set function over the items, the welfare maximization problem requires that every item be allocated to exactly one player, and one wishes to maximize the sum of values obtained by the players, as computed by applying the respective valuation function to the bundle of items allocated to the player. This problem in its full generality is NP-hard, and moreover, at least as hard to approximate as set-packing. Better approximation guarantees are known for restricted classes of valuation functions. In this work we introduce a new parameter, the supermodular degree of a valuation function, which is a measure for the extent to which the function exhibits supermodular behavior. We design an approximation algorithm for the welfare maximization problem whose approximation guarantee is linear in the supermodular degree of the underlying valuation functions.