Speeding Up q-Gram Mining on Grammar-Based Compressed Texts

We present an efficient algorithm for calculating q-gram frequencies on strings represented in compressed form, namely, as a straight line program (SLP). Given an SLP $\mathcal{T}$ of size n that represents string T, the algorithm computes the occurrence frequencies of allq-grams in T, by reducing the problem to the weighted q-gram frequencies problem on a trie-like structure of size $m = |T|-\mathit{dup}(q,\mathcal{T})$, where $\mathit{dup}(q,\mathcal{T})$ is a quantity that represents the amount of redundancy that the SLP captures with respect to q-grams. The reduced problem can be solved in linear time. Since m=O(qn), the running time of our algorithm is $O(\min\{|T|-\mathit{dup}(q,\mathcal{T}),qn\})$, improving our previous O(qn) algorithm when q=Ω(|T|/n).