Algorithms for translational tiling

Mihail N. Kolountzakis, Máté Matolcsi

Research output: Contribution to journalArticle

4 Citations (Scopus)


In this paper, we study algorithms for tiling problems. We show that the conditions (T1) and (T2) of Coven and Meyerowitz [E. Coven and A. Meyerowitz, Tiling the integers with translates of one finite set, J. Algebra 212(1) (1999), pp. 161–174], conjectured to be necessary and sufficient for a finite set A to tile the integers, can be checked in time polynomial in diam (A). We also give heuristic algorithms to find all non-periodic tilings of a cyclic group ℤN. In particular, we carry out a full classification of all non-periodic tilings of ℤ144.

Original languageEnglish
Pages (from-to)85-97
Number of pages13
JournalJournal of Mathematics and Music
Issue number2
Publication statusPublished - Jul 2009



  • Algorithms
  • Translational tiles

ASJC Scopus subject areas

  • Modelling and Simulation
  • Music
  • Computational Mathematics
  • Applied Mathematics

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