发表机构
Czech Technical University in Prague（布拉格捷克理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究分析无权连通网络微聚集问题的参数化复杂性，证明其在部分参数下可处理、部分参数下W[1]-难，还涉及内核化及有界团宽图上的NP-难性。
AI 中文摘要
网络微聚集是统计披露控制中的一项基础技术，它将图的顶点划分为满足规模约束且允许中心在有界距离内的聚类。我们研究了无权连通网络微聚集问题的参数化复杂性，重点关注结构参数和自然聚类参数，例如距离界d和聚类规模差u−l。我们证明，与加权变体不同，当以邻域多样性为参数时，无权连通问题是固定参数可处理的，因此以顶点覆盖为参数时也是如此。相比之下，对于更一般的结构参数，包括删除顶点以得到路径、星和团，该问题仍然是W[1]-难的。这些难处理性结果对于每个d≥2和任意固定的差u−l都成立，表明这些聚类参数无法克服结构难处理性。我们进一步证明，添加聚类规模界u可恢复树宽和聚类顶点删除等结构参数的可处理性，而且u是必不可少的：当单独考虑这些结构参数时，该问题仍然是W[1]-难的。对于内核化，我们证明，除非coNP⊆NP/poly，否则该问题不存在以顶点覆盖为参数的多项式内核，即使距离约束是空的也是如此。添加u可得到以顶点覆盖为参数的多项式内核，而即使结合u，对于更一般的结构参数，内核化仍然不太可能。最后，我们证明该问题在有界团宽图上是NP-难的。
英文摘要
Network microaggregation is a fundamental technique in statistical disclosure control, where vertices of a graph are partitioned into clusters satisfying size constraints and admitting a center within bounded distance. We study the parameterized complexity of the \emph{unweighted Connected Network Microaggregation} problem, focusing on structural parameters and natural clustering parameters such as the distance bound $d$ and cluster size gap $u-\ell$. We show that, unlike the weighted variant, the unweighted connected problem is fixed-parameter tractable when parameterized by neighborhood diversity, and hence by vertex cover. In contrast, it remains $\mathrm{W[1]}$-hard for more general structural parameters, including vertex deletion to paths, stars, and cliques. These hardness results hold even for every $d\ge 2$ and any fixed gap $u-\ell$, showing that these clustering parameters do not overcome the structural hardness. We further show that adding the cluster size bound $u$ restores tractability for structural parameters such as treewidth and cluster vertex deletion. Moreover, $u$ is essential: the problem remains $\mathrm{W[1]}$-hard when these structural parameters are considered alone. For kernelization, we prove that the problem has no polynomial kernel parameterized by vertex cover unless $\mathrm{coNP}\subseteq\mathrm{NP/poly}$, even when the distance constraint is vacuous. Adding $u$ yields a polynomial kernel for vertex cover, while kernelization remains unlikely for more general structural parameters even when combined with $u$. Finally, we show that the problem is NP-hard on graphs of bounded clique-width.
