Abstract
The online squarefree recognition problem is to detect the first occurrence of a square in a string whose characters are provided as input one at a time. We present an efficient algorithm to solve this problem for strings over arbitrarily ordered alphabets. Its running time is O(n log n), where n is the ending position of the first square, which matches the running times of the fastest known algorithms for the analogous offline problem. We also present a very simple algorithm for a dynamic version of the problem over general alphabets in which we are initially given a squarefree string, followed by a series of updates, and the objective is to determine after each update if the resulting string contains a square and if so, report it and stop.
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Jansson, J., Peng, Z. (2005). Online and Dynamic Recognition of Squarefree Strings. In: Jȩdrzejowicz, J., Szepietowski, A. (eds) Mathematical Foundations of Computer Science 2005. MFCS 2005. Lecture Notes in Computer Science, vol 3618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549345_45
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DOI: https://doi.org/10.1007/11549345_45
Publisher Name: Springer, Berlin, Heidelberg
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