We present hardness of approximation results for Correlation Clustering with local objectives and for Hierarchical Clustering with dissimilarity information. For the former, we study the local objective of Puleo and Milenkovic (ICML '16) that prioritizes reducing the disagreements at data points that are worst off and for the latter we study the maximization version of Dasgupta's cost function (STOC '16). Our APX hardness results imply that the two problems are hard to approximate within a constant of 4/3 ~ 1.33 (assuming P vs NP) and 9159/9189 ~ 0.9967 (assuming the Unique Games Conjecture) respectively.

中文翻译：

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局部相关聚类和相异层次聚类的不近似性

我们提出了具有局部目标的相关聚类和具有不同信息的分层聚类的近似结果的硬度。对于前者，我们研究了 Puleo 和 Milenkovic (ICML '16) 的本地目标，该目标优先减少最差数据点的分歧，而对于后者，我们研究了 Dasgupta 成本函数 (STOC '16) 的最大化版本。我们的 APX 硬度结果意味着这两个问题很难分别在 4/3 ~ 1.33（假设 P vs NP）和 9159/9189 ~ 0.9967（假设独特博弈猜想）的常数内近似。