Longest Property-Preserved Common Factor

Lorraine A. K Ayad; Giulia Bernardini; Roberto Grossi; Costas S. Iliopoulos; Nadia Pisanti; Solon P. Pissis; Giovanna Rosone

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arXiv · 1810.02099

Longest Property-Preserved Common Factor

Lorraine A. K Ayad·Giulia Bernardini·Roberto Grossi·Costas S. Iliopoulos·Nadia Pisanti·Solon P. Pissis·Giovanna Rosone

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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 $1 < k'\leq k$ 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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Lorraine A. K Ayad, Giulia Bernardini, Roberto Grossi, Costas S. Iliopoulos, Nadia Pisanti, Solon P. Pissis, Giovanna Rosone. 2018-10-04. Longest Property-Preserved Common Factor. https://arxiv.org/abs/1810.02099

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