We study two variants of the fundamental problem of finding a cluster in incomplete data. In the problems under consideration, we are given a multiset of incomplete $d$-dimensional vectors over the binary domain and integers $k$ and $r$, and the goal is to complete the missing vector entries so that the multiset of complete vectors either contains (i) a cluster of $k$ vectors of radius at most $r$, or (ii) a cluster of $k$ vectors of diameter at most $r$. We give tight characterizations of the parameterized complexity of the problems under consideration with respect to the parameters $k$, $r$, and a third parameter that captures the missing vector entries.

翻译：我们研究不完整数据中聚类发现这一基本问题的两个变体。在考虑的问题中，给定一个多集，包含二进制域上的不完整$d$维向量，以及整数$k$和$r$，目标是补全缺失的向量条目，使得完整向量的多集要么包含（i）半径为至多$r$的$k$个向量的聚类，要么包含（ii）直径为至多$r$的$k$个向量的聚类。我们针对参数$k$、$r$以及捕获缺失向量条目的第三个参数，给出了所考虑问题的参数化复杂性的紧致刻画。