Moreover, some new string kernels belonging to the family of gapped string kernels are presented, including all-length and p-length match-weighted kernels, and their variants. Based on the suffix kernel technique, we can compute all-length match-weighted kernel in time O(|s||t|), and then p-length kernel in time O(p|s||t|) using the relationship between all-length and p-length kernels. Furthermore, for p-length match-weighted kernel and its variant, a bit-parallel technique is used to reduce the complexity from O(p|s||t|) to O(pk/w
|s||t|), where w is the word size of the machine (e.g. 32 or 64 in practice) and k is determined by the longest matching subsequence of two strings s and t. The empirical results suggest that the suffix kernel technique is an important and useful approach to computing gapped string kernels.