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String Kernel (SK) techniques, especially those using gapped $k$-mers asfeatures (gk), have obtained great success in classifying sequences like DNA,protein, and text. However, the state-of-the-art gk-SK runs extremely slow whenwe increase the dictionary size ($\Sigma$) or allow more mismatches ($M$). Thisis because current gk-SK uses a trie-based algorithm to calculate co-occurrenceof 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 ofsubstrings using cumulative counting. This algorithm is fast, scalable tolarger $\Sigma$ and $M$, and naturally parallelizable. We provide a rigorousasymptotic analysis that compares GaKCo with the state-of-the-art gk-SK.Theoretically, the time cost of GaKCo is independent of the $\Sigma^{M}$ termthat slows down the trie-based approach. Experimentally, we observe that GaKCoachieves the same accuracy as the state-of-the-art and outperforms its speed byfactors 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}

GaKCo: a Fast GApped k-mer string Kernel using COunting