Abstract
We consider the following allocation problem arising in the setting of combinatorial auctions: a set of goods is to be allocated to a set of players so as to maximize the sum of the utilities of the players (i.e., the social welfare). In the case when the utility of each player is a monotone submodular function, we prove that there is no polynomial time approximation algorithm which approximates the maximum social welfare by a factor better than 1−1/e≃0.632, unless P=NP. Our result is based on a reduction from a multi-prover proof system for MAX-3-COLORING.
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This work was performed when all authors were at the Georgia Institute of Technology. A preliminary version of this work appears in Khot et al. (Workshop on internet and network economics, pp. 92–101, 2005)
R.J. Lipton’s research supported by NSF grant CCF-0431023.
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Khot, S., Lipton, R.J., Markakis, E. et al. Inapproximability Results for Combinatorial Auctions with Submodular Utility Functions. Algorithmica 52, 3–18 (2008). https://doi.org/10.1007/s00453-007-9105-7
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DOI: https://doi.org/10.1007/s00453-007-9105-7