Approximate Periods of Strings
CPM '99 Proceedings of the 10th Annual Symposium on Combinatorial Pattern Matching
Optimal discovery of repetitions in 2D
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
An efficient algorithm for online square detection
Theoretical Computer Science - Computing and combinatorics
Repetitions detection on a linear array with reconfigurable pipelined bus system
International Journal of Parallel, Emergent and Distributed Systems
Optimal discovery of repetitions in 2D
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Testing square-freeness of strings compressed by balanced straight line program
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
An efficient algorithm to test square-freeness of strings compressed by straight-line programs
Information Processing Letters
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An optimal $O(\log\log n)$-time concurrent-read concurrent-write parallel algorithm for detecting all squares in a string is presented. A tight lower bound shows that over general alphabets, this is the fastest possible optimal algorithm. When $p$ processors are available, the bounds become $\Theta(\lceil{({n\log n})/ p}\rceil + \log\log_{\lceil 1+p/n \rceil} 2p)$. The algorithm uses an optimal parallel string-matching algorithm together with periodicity properties to locate the squares within the input string.