We consider the {\em vector partition problem}, where $n$ agents, each with a $d$-dimensional attribute vector, are to be partitioned into $p$ parts so as to minimize cost which is a given function on the sums of attribute vectors in each part. The problem has applications in a variety of areas including clustering, logistics and health care. We consider the complexity and parameterized complexity of the problem under various assumptions on the natural parameters $p,d,a,t$ of the problem where $a$ is the maximum absolute value of any attribute and $t$ is the number of agent types, and raise some of the many remaining open problems.

中文翻译：

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向量划分的复杂性

我们考虑 {\em 向量划分问题}，其中 $n$ 代理，每个代理具有 $d$ 维属性向量，将被划分为 $p$ 部分，以便最小化成本，这是总和上的给定函数每个部分的属性向量。该问题在多个领域都有应用，包括集群、物流和医疗保健。我们在问题的自然参数 $p,d,a,t$ 的各种假设下考虑问题的复杂性和参数化复杂性，其中 $a$ 是任何属性的最大绝对值，$t$ 是代理的数量类型，并提出了许多剩余的未解决问题中的一些。