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Given a finite set of patterns, i.e., subsets of ZZ 2 . What is the best way to place translates of them in such a way that every point belongs to at least one translate and no two points belong to the same set of translates? We give some general results, and investigate the particular case when there is only a single pattern and that pattern is a square or has size at most four.

On Identification in ZZ2 Using Translates of Given Patterns