10.46298/dmtcs.517
Karhumaki, Juhani
Juhani
Karhumaki
Lifshits, Yury
Yury
Lifshits
Rytter, Wojciech
Wojciech
Rytter
Tiling Periodicity
episciences.org
2010
algorithms on word
periodicities
tilers
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
contact@episciences.org
episciences.org
2015-03-26T16:21:11+01:00
2021-08-23T23:09:24+02:00
2010-01-01
en
Journal article
https://dmtcs.episciences.org/517
https://hal.archives-ouvertes.fr/hal-00990466v1
1365-8050
PDF
1
Discrete Mathematics & Theoretical Computer Science ; Vol. 12 no. 2 ; 1365-8050
International audience
We contribute to combinatorics and algorithmics of words by introducing new types of periodicities in words. A tiling period of a word w is partial word u such that w can be decomposed into several disjoint parallel copies of u, e.g. a lozenge b is a tiling period of a a b b. We investigate properties of tiling periodicities and design an algorithm working in O(n log (n) log log (n)) time which finds a tiling period of minimal size, the number of such minimal periods and their compact representation. The combinatorics of tiling periods differs significantly from that for classical full periods, for example unlike the classical case the same word can have many different primitive tiling periods. We consider also a related new type of periods called in the paper multi-periods. As a side product of the paper we solve an open problem posted by T. Harju (2003).