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A Unifying look at d-dimensional periodicities ans space covering

Mireille Regnier 1 L. Rostami
1 ALGO - Algorithms
Inria Paris-Rocquencourt
Abstract : We propose a formal characterization of d-dimensional periodicities. We show first that any periodic pattern has a canonical decomposition and a minimal generator, generalizing the 1D property. This allows to classify the d-dimensional patterns in d+1 classes, according to their periodicities, each class having subclasses. A full classification of the coverings of a 2-dimensional space by a pattern follows. These results have important algorithmic issues in pattern matching. First, the covering classification allows an efficient use of the now classical duel paradigm. Second, d-dimensional pattern matching complexity is intrinsically different for each class.
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Submitted on : Wednesday, May 24, 2006 - 3:59:48 PM
Last modification on : Thursday, February 3, 2022 - 11:14:31 AM
Long-term archiving on: : Tuesday, April 12, 2011 - 6:02:44 PM


  • HAL Id : inria-00074650, version 1



Mireille Regnier, L. Rostami. A Unifying look at d-dimensional periodicities ans space covering. [Research Report] RR-2021, INRIA. 1993. ⟨inria-00074650⟩



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