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CORR
2012
Springer

On the Hardness of Welfare Maximization in Combinatorial Auctions with Submodular Valuations

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On the Hardness of Welfare Maximization in Combinatorial Auctions with Submodular Valuations
We present a new type of monotone submodular functions: multi-peak submodular functions. Roughly speaking, given a family of sets F, we construct a monotone submodular function f with a high value f(S) for every set S ∈ F (a “peak”), and a low value on every set that does not intersect significantly any set in F. We use this construction to show that a better than (1 − 1 2e )-approximation ( 0.816) for welfare maximization in combinatorial auctions with submodular valuations is (1) impossible in the communication model, (2) NP-hard in the computational model where valuations are given explicitly. Establishing a constant approximation hardness for this problem in the communication model was a long-standing open question. The valuations we construct for the hardness result in the computational model depend only on a constant number of items, and hence the result holds even if the players can answer arbitrary queries about their valuation, including demand queries. We also study...
Shahar Dobzinski, Jan Vondrák
Added 20 Apr 2012
Updated 20 Apr 2012
Type Journal
Year 2012
Where CORR
Authors Shahar Dobzinski, Jan Vondrák
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