A unifying look at d-dimensional periodicities and space coverings

  • Mireille Régnier
  • Ladan Rostami
Conference paper

DOI: 10.1007/BFb0029807

Part of the Lecture Notes in Computer Science book series (LNCS, volume 684)
Cite this paper as:
Régnier M., Rostami L. (1993) A unifying look at d-dimensional periodicities and space coverings. In: Apostolico A., Crochemore M., Galil Z., Manber U. (eds) Combinatorial Pattern Matching. CPM 1993. Lecture Notes in Computer Science, vol 684. Springer, Berlin, Heidelberg

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 2d−1 + 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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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Mireille Régnier
    • 1
  • Ladan Rostami
    • 2
  1. 1.INRIALe ChesnayFrance
  2. 2.LITPParis Cedex 05France

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