We give tolerant testers with sublinear query complexity in the adjacency-list model for Unique Games. Prior tolerant testers required structural assumptions such as expansion or clusterability. For Unique Games, the tester distinguishes instances whose optimum fraction of violated constraints is at most $\varepsilon$ from those whose optimum is at least $ρ$, for $0<\varepsilon<ρ<1$, assuming $\varepsilon\log n\lesssimρ^4$. On instances with $n$ vertices and $m$ constraints, it uses $\widetilde O(\sqrt m\,ρ^{-13/2}+nρ^{-2}/\sqrt m)$ queries. We also give a specialized tester for bipartiteness, the $Q=2$ transposition case of Unique Games. Exploiting its signed structure, the tester achieves substantially better tolerance and query-complexity guarantees than the generic Unique Games tester. Writing $λ=ρ/(1+\log(1/ρ))$, the bipartiteness tester distinguishes graphs that can be made bipartite by deleting at most an $\varepsilon$ fraction of edges from graphs in which every bipartition has at least a $ρ$ fraction of edges with both endpoints on the same side, assuming $\varepsilon\log n\lesssimλ^2$, using $\widetilde O(\sqrt m/λ^2+n/(\sqrt m\,λ))$ queries.

翻译：我们给出邻接表模型下唯一游戏的容忍性测试器，其查询复杂度为次线性。先前的容忍性测试器需要诸如扩展性或可聚类性等结构假设。对于唯一游戏，该测试器能够区分最优违规约束比例至多为$\varepsilon$的实例与最优比例至少为$ρ$的实例，其中$0<\varepsilon<ρ<1$，且假设$\varepsilon\log n\lesssimρ^4$。在具有$n$个顶点和$m$个约束的实例上，它使用$\widetilde O(\sqrt m\,ρ^{-13/2}+nρ^{-2}/\sqrt m)$次查询。我们还给出一个专门用于二部性（唯一游戏中$Q=2$的转置情况）的测试器。通过利用其符号结构，该测试器在容忍性和查询复杂度保证上显著优于通用唯一游戏测试器。记$λ=ρ/(1+\log(1/ρ))$，该二部性测试器能够区分可通过删除至多$\varepsilon$比例边而转化为二部图的图（其中每个二划分都至少有$ρ$比例的边两端点位于同侧），假设$\varepsilon\log n\lesssimλ^2$，使用$\widetilde O(\sqrt m/λ^2+n/(\sqrt m\,λ))$次查询。