  Sequential pattern mining (SPM) has excellent prospects and application
spaces and has been widely used in different fields. The non-overlapping SPM,
as one of the data mining techniques, has been used to discover patterns that
have requirements for gap constraints in some specific mining tasks, such as
bio-data mining. And for the non-overlapping sequential patterns with gap
constraints, the Nettree structure has been proposed to efficiently compute the
support of the patterns. For pattern mining, users usually need to consider the
threshold of minimum support (\textit{minsup}). This is especially difficult in
the case of large databases. Although some existing algorithms can mine the
top-$k$ patterns, they are approximate algorithms with fixed lengths. In this
paper, a precise algorithm for mining \underline{T}op-$k$
\underline{N}on-\underline{O}verlapping \underline{S}equential
\underline{P}atterns (TNOSP) is proposed. The top-$k$ solution of SPM is an
effective way to discover the most frequent non-overlapping sequential patterns
without having to set the \textit{minsup}. As a novel pattern mining algorithm,
TNOSP can precisely search the top-$k$ patterns of non-overlapping sequences
with different gap constraints. We further propose a pruning strategy named
\underline{Q}ueue \underline{M}eta \underline{S}et \underline{P}runing (QMSP)
to improve TNOSP's performance. TNOSP can reduce redundancy in non-overlapping
sequential mining and has better performance in mining precise non-overlapping
sequential patterns. The experimental results and comparisons on several
datasets have shown that TNOSP outperformed the existing algorithms in terms of
precision, efficiency, and scalability.
