Deterministic Sparse Suffix Sorting in the Restore Model

Given a text $T$ of length $n$, we propose a deterministic online algorithm computing the sparse suffix array and the sparse longest common prefix array of $T$ in $O(c\sqrt{\lg n}+m\lg m\lg n{\lg }^{\ast }n)$ time with $O(m)$ words of space under the premise that the space of $T$ is rewritable, where $m\le n$ is the number of suffixes to be sorted (provided online and arbitrarily), and $c$ is the number of characters with $m\le c\le n$ that must be compared for distinguishing the designated suffixes.