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Longest property-preserved common factor: A new string-processing framework

Abstract : We introduce a new family of string processing problems. Given two or more strings, we are asked to compute a factor common to all strings that preserves a specific property and has maximal length. We consider three fundamental string properties: square-free factors, periodic factors, and palindromic factors under three different settings, one per property. In the first setting, we are given a string x and we are asked to construct a data structure over x answering the following type of online queries: given a string y, find a longest square-free factor common to x and y. In the second setting, we are given k strings and an integer 1 < k ≤ k and we are asked to find a longest periodic factor common to at least k strings. In the third one, we are given two strings and we are asked to find a longest palindromic factor common to the two strings. We present linear-time solutions for all settings. This is a full and extended version of a paper from SPIRE 2018.
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Submitted on : Friday, October 2, 2020 - 2:15:25 PM
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Lorraine A.K. Ayad, Giulia Bernardini, Roberto Grossi, Costas Iliopoulos, Nadia Pisanti, et al.. Longest property-preserved common factor: A new string-processing framework. Theoretical Computer Science, Elsevier, 2020, 812, pp.244-251. ⟨10.1016/j.tcs.2020.02.012⟩. ⟨hal-02956135⟩



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