Faster Algorithms for Internal Dictionary Queries

In this paper, we consider the problem of preprocessing a text $T$ of length $n$ and a dictionary $\mathcal{D}$ to answer multiple types of pattern queries. Inspired by [Charalampopoulos-Kociumaka-Mohamed-Radoszewski-Rytter-Wale\'n ISAAC 2019], we consider the Internal Dictionary, where the dictionary is interval in the sense that every pattern is given as a fragment of $T$. Therefore, the size of $\mathcal{D}$ is proportional to the number of patterns instead of their total length, which could be $\Theta(n \cdot |\mathcal{D}|)$. We propose a new technique to preprocess $T$ and organize the substring structure. In this way, we are able to develop algorithms to answer queries more efficiently than in previous works.