Unbordered Pictures: Properties and Construction

  • Marcella Anselmo
  • Dora Giammarresi
  • Maria MadoniaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9270)


The notion of unbordered picture generalizes to two dimensions the notion of unbordered (or bifix-free) string. We extend to two dimensions Nielsen’s construction of unbordered strings ([23]) and describe an algorithm to construct the set U(mn) of unbordered pictures of fixed size (mn). The algorithm recursively computes the set of quasi-unbordered pictures Q(mn), i.e. pictures that can possibly have some “large” borders.


Bifix-free strings Unbordered pictures 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Marcella Anselmo
    • 1
  • Dora Giammarresi
    • 2
  • Maria Madonia
    • 3
    Email author
  1. 1.Dipartimento di InformaticaUniversità di SalernoFiscianoItaly
  2. 2.Dipartimento di MatematicaUniversità Roma “Tor Vergata”RomaItaly
  3. 3.Dipartimento di Matematica e InformaticaUniversità di CataniaCataniaItaly

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