NDLI: On Maximizing Welfare When Utility Functions Are Subadditive

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Feige, Uriel
Copyright Year	2009
Abstract	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. 610618]. 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. 10641073], 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.
Starting Page	122
Ending Page	142
Page Count	21
File Format	PDF
ISSN	00975397
DOI	10.1137/070680977
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	1 (Special Issue On The Thirty-Eighth Annual ACM Symposium On Theory Of Computing (STOC 2006))
Volume Number	39
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-05-28
Access Restriction	Subscribed
Subject Keyword	combinatorial auctions Approximation algorithms linear programming approximation algorithms randomized rounding Combinatorial optimization
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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