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- W2964758001 abstract "The 2-to-2 Games Theorem of [16, 10, 11, 17] implies that it is NP-hard to distinguish between Unique Games instances with assignment satisfying at least (1/2 - e) fraction of the constraints vs. no assignment satisfying more than e fraction of the constraints, for every constant e > 0. We show that the reduction can be transformed in a non-trivial way to give a stronger guarantee in the completeness case: For at least (1/2 - e) fraction of the vertices on one side, all the constraints associated with them in the Unique Games instance can be satisfied.We use this guarantee to convert the known UG-hardness results to NP-hardness. We show:1. Tight inapproximability of approximating independent sets in degree d graphs within a factor of [EQUATION], where d is a constant.2. NP-hardness of approximate the Maximum Acyclic Subgraph problem within a factor of 2/3 + e, improving the previous ratio of 14/15 + e by Austrin et al. [4].3. For any predicate P-1(1) ⊆ [q]k supporting a balanced pairwise independent distribution, given a P-CSP instance with value at least 1/2 - e, it is NP-hard to satisfy more than [EQUATION] fraction of constraints." @default.
- W2964758001 created "2019-08-13" @default.
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- W2964758001 date "2019-07-17" @default.
- W2964758001 modified "2023-09-23" @default.
- W2964758001 title "UG-hardness to NP-hardness by losing half" @default.
- W2964758001 doi "https://doi.org/10.4230/lipics.ccc.2019.3" @default.
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