String regularities with don't cares

Authors:
Costas S. Iliopoulos;Manal Mohamed;Laurent Mouchard;W. F. Smyth;Katerina G. Perdikuri;Athanasios K. Tsakalidis
Affiliations:
Department of Computer Science, King's College London, London WC2R 2LS, England;Department of Computer Science, King's College London, London WC2R 2LS, England;Department of Vegetal Physiology -- ABISS Université de Rouen, 76821 Mont Saint Aignan Cedex, France;Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada L8S 4K7 and School of Computing, Curtin University, GPO Box U-1987, Perth WA 6845, Australia;Research Academic Computer Technology Institute (RACTI), 61 Riga Feraiou str., 26221, Patras, Greece;Research Academic Computer Technology Institute (RACTI), 61 Riga Feraiou str., 26221, Patras, Greece
Venue:
Nordic Journal of Computing - Special issue: Selected papers of the Prague Stringology conference (PSC'02), September 23-24, 2002
Year:
2003

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Abstract

We describe algorithms for computing typical regularities in strings x = x[1..n] that contain don't care symbols. For such strings on alphabet Σ, an O(n log n log |Σ|) 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.