Algorithms for translational tiling

Mihail N. Kolountzakis, Máté Matolcsi

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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
Volume3
Issue number2
DOIs
Publication statusPublished - Jul 2009

    Fingerprint

Keywords

  • Algorithms
  • Translational tiles

ASJC Scopus subject areas

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

Cite this