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

*Theoretical Computer Science*( IF 0.747 )

**Pub Date : 2020-02-11**

*, DOI:*

*10.1016/j.tcs.2020.02.012*

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

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 $1<{k}^{\prime}\le k$ and we are asked to find a longest periodic factor common to at least ${k}^{\prime}$ 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.