  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.
