  As a representative sequential pattern mining problem, counting the frequency
of serial episodes from a streaming sequence has drawn continuous attention in
academia due to its wide application in practice, e.g., telecommunication
alarms, stock market, transaction logs, bioinformatics, etc. Although a number
of serial episodes mining algorithms have been developed recently, most of them
are neither stream-oriented, as they require multi-pass of dataset, nor
time-aware, as they fail to take into account the time constraint of serial
episodes. In this paper, we propose two novel one-pass algorithms, ONCE and
ONCE+, each of which can respectively compute two popular frequencies of given
episodes satisfying predefined time-constraint as signals in a stream arrives
one-after-another. ONCE is only used for non-overlapped frequency where the
occurrences of a serial episode in sequence are not intersected. ONCE+ is
designed for the distinct frequency where the occurrences of a serial episode
do not share any event. Theoretical study proves that our algorithm can
correctly mine the frequency of target time constraint serial episodes in a
given stream. Experimental study over both real-world and synthetic datasets
demonstrates that the proposed algorithm can work, with little time and space,
in signal-intensive streams where millions of signals arrive within a single
second. Moreover, the algorithm has been applied in a real stream processing
system, where the efficacy and efficiency of this work is tested in practical
applications.
