The Prague Stringology Conference 2002

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

String Regularities with Don't Cares

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

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