  String Kernel (SK) techniques, especially those using gapped $k$-mers as
features (gk), have obtained great success in classifying sequences like DNA,
protein, and text. However, the state-of-the-art gk-SK runs extremely slow when
we increase the dictionary size ($\Sigma$) or allow more mismatches ($M$). This
is because current gk-SK uses a trie-based algorithm to calculate co-occurrence
of mismatched substrings resulting in a time cost proportional to
$O(\Sigma^{M})$. We propose a \textbf{fast} algorithm for calculating
\underline{Ga}pped $k$-mer \underline{K}ernel using \underline{Co}unting
(GaKCo). GaKCo uses associative arrays to calculate the co-occurrence of
substrings using cumulative counting. This algorithm is fast, scalable to
larger $\Sigma$ and $M$, and naturally parallelizable. We provide a rigorous
asymptotic analysis that compares GaKCo with the state-of-the-art gk-SK.
Theoretically, the time cost of GaKCo is independent of the $\Sigma^{M}$ term
that slows down the trie-based approach. Experimentally, we observe that GaKCo
achieves the same accuracy as the state-of-the-art and outperforms its speed by
factors of 2, 100, and 4, on classifying sequences of DNA (5 datasets), protein
(12 datasets), and character-based English text (2 datasets), respectively.
  GaKCo is shared as an open source tool at
\url{https://github.com/QData/GaKCo-SVM}
