  The $k$-mappability problem has two integers parameters $m$ and $k$. For
every subword of size $m$ in a text $S$, we wish to report the number of
indices in $S$ in which the word occurs with at most $k$ mismatches.
  The problem was lately tackled by Alzamel et al. For a text with constant
alphabet $\Sigma$ and $k \in O(1)$, they present an algorithm with linear space
and $O(n\log^{k+1}n)$ time. For the case in which $k = 1$ and a constant size
alphabet, a faster algorithm with linear space and $O(n\log(n)\log\log(n))$
time was presented in a 2020 paper by Alzamel et al.
  In this work, we enhance the techniques of Alzamel et al.'s 2020 paper to
obtain an algorithm with linear space and $O(n \log(n))$ time for $k = 1$. Our
algorithm removes the constraint of the alphabet being of constant size. We
also present linear algorithms for the case of $k=1$, $|\Sigma|\in O(1)$ and
$m=\Omega(\sqrt{n})$.
