Labeled and Unlabeled Reconfiguration by Compaction

We consider configurations of (labeled or unlabeled) objects on an integer lattice, and their behaviour under compaction operations: we may think of these as globally pushing all objects with a horizontal or vertical half-plane by one unit, where objects will also push other objects which are in the way. Under this model, the central question is: given two configurations of the same set of objects, is there a sequence of compaction operations that will transform the first configuration into the second. In this talk, we will consider both the characterization of such configuration pairs where the answer is yes, and the computational complexity of answering this question in general as well as in some special cases.