In this work, we study the k-median clustering problem with an additional equal-size constraint on the clusters from the perspective of parameterized preprocessing. Our main result is the first lossy (2-approximate) polynomial kernel for this problem parameterized by the cost of clustering. We complement this result by establishing lower bounds for the problem that eliminate the existence of an (exact) kernel of polynomial size and a PTAS.

中文翻译：

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相同大小聚类的有损核化

在这项工作中，我们从参数化预处理的角度研究了对簇附加等大小约束的k中值聚类问题。我们的主要结果是该问题的第一个有损（2 近似）多项式内核，该问题通过聚类成本进行参数化。我们通过建立问题的下界来补充这个结果，消除多项式大小的（精确）核和 PTAS 的存在。