On data reduction for dynamic vector bin packing

We study a dynamic vector bin packing (DVBP) problem. We show hardness for shrinking arbitrary DVBP instances to size polynomial in the number of request types or in the maximal number of requests overlapping in time. We also present a simple polynomial-time data reduction algorithm that allows to recover $(1 + {\varepsilon})$-approximate solutions for arbitrary ${\varepsilon} > 0$. It shrinks instances from Microsoft Azure and Huawei Cloud by an order of magnitude for ${\varepsilon} = 0.02$.

翻译：我们研究一个动态矢量垃圾包装问题。 我们表现出了缩小任意的 DVBP 实例的难度, 以请求类型数量或最大数量的时间重叠请求大小为多等量。 我们还提出了一个简单的多等时间数据减少算法, 它可以收回$(1 + pravepsilon} $- 近似解决方案, 任意的 $ = $ = 0。 它将微软 Azure 和华威云 的事例压缩为 $ = 0.02 美元 。