Abstract
Consider the following decision problem. Given a collection of non-overlapping (but possibly touching) polygons in the plane, is there a proper connected subcollection of it that can be separated from its complement moving as a rigid body, without disturbing the other parts of the collection, and such that the complement is also connected? We show that this decision problem is NP-complete. This had been known to be true without the connectedness requirement, and also with this requirement but in three-dimensional space.
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