Improved competitive ratios for submodular secretary problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
ESA'11 Proceedings of the 19th European conference on Algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Welfare guarantees for combinatorial auctions with item bidding
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Budget feasible mechanism design: from prior-free to bayesian
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Combinatorial auctions with restricted complements
Proceedings of the 13th ACM Conference on Electronic Commerce
Santa claus meets hypergraph matchings
ACM Transactions on Algorithms (TALG)
Online mechanism design (randomized rounding on the fly)
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Welfare maximization and the supermodular degree
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Simultaneous auctions are (almost) efficient
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Annals of Mathematics and Artificial Intelligence
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We consider the problem of maximizing welfare when allocating $m$ items to $n$ players with subadditive utility functions. Our main result is a way of rounding any fractional solution to a linear programming relaxation to this problem so as to give a feasible solution of welfare at least $1/2$ that of the value of the fractional solution. This approximation ratio of $1/2$ is an improvement over an $\Omega(1/\log m)$ ratio of Dobzinski, Nisan, and Schapira [Proceedings of the 37th Annual ACM Symposium on Theory of Computing (Baltimore, MD), ACM, New York, 2005, pp. 610-618]. We also show an approximation ratio of $1-1/e$ when utility functions are fractionally subadditive. A result similar to this last result was previously obtained by Dobzinski and Schapira [Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (Miami, FL), SIAM, Philadelphia, 2006, pp. 1064-1073], but via a different rounding technique that requires the use of a so-called “XOS oracle.” The randomized rounding techniques that we use are oblivious in the sense that they only use the primal solution to the linear program relaxation, but have no access to the actual utility functions of the players.