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
Nearby in the stack
, 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∣logσ)
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.