Algorithms for translational tiling

Kolountzakis, M. N. and Matolcsi, Máté (2009) Algorithms for translational tiling. JOURNAL OF MATHEMATICS AND MUSIC, 3 (2). pp. 85-97. ISSN 1745-9737

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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 Z(N). In particular, we carry out a full classification of all non-periodic tilings of Z(144).

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