String regularities with don't cares

Costas S. Iliopoulos, Manal Mohamed, Laurent Mouchard, Katerina Perdikuri, William F. Smyth, Athanasios K. Tsakalidis

Research output: Contribution to journalArticlepeer-review


We describe algorithms for computing typical regularities in strings x = x[1.n] that contain don't care symbols. For such strings on alphabet Sigma, an O(n log n log | Sigma |) worst-case time algorithm for computing the period is known, but the algorithm is impractical due to a large constant of proportionality. We present instead two simple practical algorithms that compute all the periods of every prefix of x; our algorithms require quadratic worst-case time but only linear time in the average case. We then show how our algorithms can be used to compute other string regularities, specifically the covers of both ordinary and circular strings. (17 References).
Original languageEnglish
Pages (from-to)40 - 51
Number of pages12
JournalNordic Journal of Computing
Issue number1
Publication statusPublished - 2003


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