Maximum constraint satisfaction problem (Max-CSP) is a rich class of combinatorial optimization problems. In this dissertation, we show optimal (up to a constant factor) NP-hardness for maximum constraint satisfaction problem with k variables per constraint (Max-k-CSP), whenever k is larger than the domain size. This follows from our main result concerning CSPs given by a predicate: a CSP is approximation resistant if its predicate contains a subgroup that is balanced pairwise independent. Our main result is related to previous works conditioned on the Unique-Games Conjecture and integrality gaps in sum-of-squares semidefinite programming hierarchies. Our main ingredient is a new gap-amplification technique inspired by XOR-lemmas. Using this technique, we also improve the NP-hardness of approximating Independent-Set on bounded-degree graphs, Almost-Coloring, Two-Prover-One-Round-Game, and various other problems.
Title
Hardness of Maximum Constraint Satisfaction
Published
2013-05-13
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
EECS-2013-57
Type
Text
Extent
58 p
Archive
The Engineering Library
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