For rearranging objects on tabletops with overhand grasps, temporarily relocating objects to some buffer space may be necessary. This raises the natural question of how many simultaneous storage spaces, or "running buffers", are required so that certain classes of tabletop rearrangement problems are feasible. In this work, we examine the problem for both labeled and unlabeled settings. On the structural side, we observe that finding the minimum number of running buffers (MRB) can be carried out on a dependency graph abstracted from a problem instance, and show that computing MRB is NP-hard. We then prove that under both labeled and unlabeled settings, even for uniform cylindrical objects, the number of required running buffers may grow unbounded as the number of objects to be rearranged increases. We further show that the bound for the unlabeled case is tight. On the algorithmic side, we develop effective exact algorithms for finding MRB for both labeled and unlabeled tabletop rearrangement problems, scalable to over a hundred objects under very high object density. More importantly, our algorithms also compute a sequence witnessing the computed MRB that can be used for solving object rearrangement tasks. Employing these algorithms, empirical evaluations reveal that random labeled and unlabeled instances, which more closely mimics real-world setups, generally have fairly small MRBs. Using real robot experiments, we demonstrate that the running buffer abstraction leads to state-of-the-art solutions for in-place rearrangement of many objects in tight, bounded workspace.

翻译：对于使用上抓取方式重新排列桌面上的物体，可能需要将物体临时移动到某些缓冲区空间。这自然引发了一个问题：需要多少个同时存储空间（即“运行缓冲区”）才能确保特定类别的桌面重排问题具有可行性。在本工作中，我们研究了有标签和无标签两种设定下的问题。在结构方面，我们观察到，求取最小运行缓冲区数（MRB）可以在从问题实例抽象出的依赖图上进行，并证明计算MRB是NP难的。我们进一步证明，在有标签和无标签两种设定下，即使对于均匀圆柱形物体，所需运行缓冲区数量可能随着待重排物体数量的增加而无界增长，并表明无标签情况下的界限是紧的。在算法方面，我们开发了有效的精确算法来求解有标签和无标签桌面重排问题的MRB，该算法可扩展至超过一百个物体且物体密度极高的情况。更重要的是，我们的算法还计算出一个见证所求MRB的序列，可用于解决物体重排任务。利用这些算法，实证评估揭示，随机生成的有标签和无标签实例（更接近真实场景）通常具有相当小的MRB。通过真实机器人实验，我们证明运行缓冲区抽象为在紧凑、有界工作空间中原地重排大量物体提供了最先进的解决方案。