Optimal superprimitivity testing for strings
Information Processing Letters
Partial words and a theorem of Fine and Wilf
Theoretical Computer Science
On the Periods of Partial Words
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
String regularities with don't cares
Nordic Journal of Computing - Special issue: Selected papers of the Prague Stringology conference (PSC'02), September 23-24, 2002
The Art of Computer Programming, Volume 4, Fascicle 3: Generating All Combinations and Partitions
The Art of Computer Programming, Volume 4, Fascicle 3: Generating All Combinations and Partitions
Many aspects of defect theorems
Theoretical Computer Science - Words, languages and combinatorics
Bases of Motifs for Generating Repeated Patterns with Wild Cards
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Tiling an interval of the discrete line
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
| Hi-index | 0.00 |
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 ⋄ b is a tiling period of aabb. 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 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.