Algorithms for translational tiling
Mihail N. Kolountzakis, Mate Matolcsi

TL;DR
This paper develops polynomial-time algorithms to verify Coven-Meyerowitz conditions for tiling integers and introduces heuristic methods for classifying non-periodic tilings of cyclic groups, including a complete classification of Z_144.
Contribution
It provides the first polynomial-time algorithms for checking tiling conditions and offers heuristic algorithms for classifying non-periodic tilings, with a full classification of Z_144.
Findings
Conditions (T1) and (T2) can be checked in polynomial time.
Heuristic algorithms effectively find non-periodic tilings.
Complete classification of non-periodic tilings of Z_144.
Abstract
In this paper we study algorithms for tiling problems. We show that the conditions and of Coven and Meyerowitz, conjectured to be necessary and sufficient for a finite set to tile the integers, can be checked in time polynomial in . We also give heuristic algorithms to find all non-periodic tilings of a cyclic group . In particular we carry out a full classification of all non-periodic tilings of .
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Taxonomy
TopicsCellular Automata and Applications · Quasicrystal Structures and Properties · Color Science and Applications
