  Given a text $T$ and a pattern $P$, the order-preserving matching problem is
to find all substrings in $T$ which have the same relative orders as $P$.
Order-preserving matching has been an active research area since it was
introduced by Kubica et al. \cite{kubica2013linear} and Kim et al.
\cite{kim2014order}. In this paper we present two algorithms for the multiple
order-preserving matching problem, one of which runs in sublinear time on
average and the other in linear time on average. Both algorithms run much
faster than the previous algorithms.
