Longest Property-Preserved Common Factor

Abstract : In this paper we introduce a new family of string processing problems. We are given two or more strings and we are asked to compute a factor common to all strings that preserves a specific property and has maximal length. Here 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 on-line queries: given 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 setting, 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. We anticipate that our paradigm can be extended to other string properties or settings.
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Submitted on : Tuesday, November 13, 2018 - 9:18:39 PM
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Lorraine Ayad, Giulia Bernardini, Roberto Grossi, Costas Iliopoulos, Nadia Pisanti, et al.. Longest Property-Preserved Common Factor. International Symposium on String Processing and Information Retrieval, 2018, Lima, Peru. ⟨hal-01921603⟩

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