In binary unbiased local coordination games, average disagreement ≤ ε implies the graph is (O(ε log(1/ε)), r)-amenable.
Approximation Algorithms for Classification Problems with Pairwise Relationships: Metric Labeling and Markov Random Fields.Journal of the ACM, 49(5):616–639, 2002
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Improved Amenability Bounds for Local Coordination Games
In binary unbiased local coordination games, average disagreement ≤ ε implies the graph is (O(ε log(1/ε)), r)-amenable.