From query complexity to computational complexity

We consider submodular optimization problems, and provide a general way of translating oracle inapproximability results arising from the symmetry gap technique to computational complexity inapproximability results, where the submodular function is given explicitly (under the assumption that NP = RP). Applications of our technique include an optimal computational hardness of (1 2 + )-approximation for maximizing a symmetric nonnegative submodular function, an optimal hardness of (1−(1−1/k)k + )-approximation for welfare maximization in combinatorial auctions with k submodular bidders (for constant k), super-constant hardness for maximizing a nonnegative submodular function over matroid bases, and tighter bounds for maximizing a monotone submodular function subject to a cardinality constraint. Unlike the vast majority of computational inapproximability results, our approach does not use the PCP machinery or the Unique Games Conjecture, but relies instead on a direct reduction from U...

• Type: Journal
• Year: 2012
• Where: STOC
• Authors: Shahar Dobzinski, Jan Vondrák
• Keywords: Algorithms, Cardinality Constraint, Combinatorial Auctions, Rp Applications, STOC 2012