The sliding cubes model is a well-established theoretical framework that supports the analysis of reconfiguration algorithms for modular robots consisting of face-connected cubes. The best algorithm currently known for the reconfiguration problem, by Abel and Kominers [arXiv, 2011], uses O(n3) moves to transform any n-cube configuration into any other n-cube configuration. As is common in the literature, this algorithm reconfigures the input into an intermediate canonical shape. In this paper we present an in-place algorithm that reconfigures any n-cube configuration into a compact canonical shape using a number of moves proportional to the sum of coordinates of the input cubes. This result is asymptotically optimal. Furthermore, our algorithm directly extends to dimensions higher than three.

翻译：滑动立方体模型是一个成熟的理论框架，用于支持由面连接立方体组成的模块化机器人重配置算法的分析。目前已知解决重配置问题的最佳算法由Abel和Kominers提出[arXiv, 2011]，该算法使用O(n³)次移动将任意n立方体配置转换为任意其他n立方体配置。与该领域的常规做法一致，该算法先将输入配置重配置为一种中间规范形状。本文提出一种原位算法，能够使用与输入立方体坐标之和成比例的移动次数，将任意n立方体配置重配置为紧凑规范形状。该结果在渐近意义下是最优的。此外，我们的算法可直接推广到三维以上的高维空间。