On Longest Common Property Preserved Substring Queries
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We revisit the problem of longest common property preserving substring queries introduced by Ayad et al. (SPIRE 2018, arXiv 2018). We consider a generalized and unified on-line setting, where we are given a set X of k strings of total length n that can be pre-processed so that, given a query string y and a positive integer k'≤ k, we can determine the longest substring of y that satisfies some specific property and is common to at least k' strings in X. Ayad et al. considered the longest square-free substring in an on-line setting and the longest periodic and palindromic substring in an off-line setting. In this paper, we give efficient solutions in the on-line setting for finding the longest common square, periodic, palindromic, and Lyndon substrings. More precisely, we show that X can be pre-processed in O(n) time resulting in a data structure of O(n) size that answers queries in O(|y|σ) time and O(1) working space, where σ is the size of the alphabet, and the common substring must be a square, a periodic substring, a palindrome, or a Lyndon word.
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