Approximation algorithms for combinatorial auctions with complement-free bidders

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Approximation algorithms for combinatorial auctions with complement-free bidders (2005)

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by Shahar Dobzinski , Noam Nisan , Michael Schapira

Venue:	In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC
Citations:	133 - 25 self

BibTeX

@INPROCEEDINGS{Dobzinski05approximationalgorithms,
    author = {Shahar Dobzinski and Noam Nisan and Michael Schapira},
    title = {Approximation algorithms for combinatorial auctions with complement-free bidders},
    booktitle = {In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC},
    year = {2005},
    pages = {610--618}
}

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Abstract

We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items m and in the number of bidders n, even though the “input size ” is exponential in m. The first algorithm provides an O(log m) approximation. The second algorithm provides an O ( √ m) approximation in the weaker model of value oracles. This algorithm is also incentive compatible. The third algorithm provides an improved 2-approximation for the more restricted case of “XOS bidders”, a class which strictly contains submodular bidders. We also prove lower bounds on the possible approximations achievable for these classes of bidders. These bounds are not tight and we leave the gaps as open problems. 1

Keyphrases

combinatorial auction approximation algorithm complement-free bidder submodular bidder first algorithm complement free bidder third algorithm improved 2-approximation open problem second algorithm input size allocation problem restricted case xos bidder running time value oracle possible approximation incentive compatible

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