A Simple ( but Optimal ) 2 D -

The duel paradigm appeared in the recent years as crucial to design eecient 1D or 2D pattern matching algorithms. It relies on the computation of witnesses, i.e. mismatching positions between two overlapping copies of a pattern p searched in a text t. Although this is easily done in linear time in 1D, the two previous algorithms in 2D rely on quite intricate data structures. We prove new structural properties of 2D patterns, and provide an algorithm to derive the fundamental basis of periodicities. We show how theoretical results on 2D periodicities allow to write and implement a simple algorithm that is still linear in the size of the pattern, hence optimal.