April 20, 2017

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By N. Benvenuto, et al.,

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SIAM J. Disc. Math. 11(4), 511–523 (1998) 10. : More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP. Rand. Struct. Algo. 33(4), 497–514 (2008) 11. : Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. , New York (1979) 12. : Beating the random ordering is hard: Every ordering CSP is approximation resistant. SIAM J. Comput. 40(3), 878–914 (2011) 13. : Beating the random ordering is hard: Inapproximability of Maximum Acyclic Subgraph. In: FOCS, pp.

A (2 + )-approximation algorithm for the stochastic knapsack problem (2012) (unpublished manuscript) 5. : Improved approximation results for stochastic knapsack problems. In: SODA (2011) 6. : A ptas for the multiple knapsack problem. In: SODA (2000) Online Stochastic GAP 25 7. : Approximating the stochastic knapsack problem: The benefit of adaptivity. In: FOCS (2004) 8. : Near optimal online algorithms and fast approximation algorithms for resource allocation problems. In: EC (2011) 9. : A combinatorial allocation mechanism with penalties for banner advertising.

Finally, improving our general hardness result to only requiring that D is pairwise independent is interesting especially in light of the analogous results for CSPs [4,6]. Acknowledgement. We would like to thank Johan H˚ astad for suggesting this problem and for numerous helpful discussions regarding the same. We acknowledge ERC Advanced Grant 226203 and Swedish Research Council Grant 6212012-4546 for making this project feasible. References 1. : Subexponential algorithms for Unique Games and related problems.

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