Optimal In-Place Compaction of Sliding Cubes (Media Exposition)

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. This note accompanies a video that explains our in-place algorithm for reconfiguration in the sliding cubes model. Specifically, our algorithm [2] 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. As is common in the literature, we can then reconfigure between two arbitrary shapes via their canonical configurations. The number of moves performed by our algorithm is asymptotically worst-case optimal and strictly improves upon the current state-of-the-art.