Internal Dictionary Matching

We introduce data structures answering queries concerning the occurrences of patterns from a given dictionary $$\mathsf {D}$$ in fragments string T length n. The is internal sense that each pattern as fragment T. This way, takes space proportional to number $$d=|\mathsf {D}|$$ rather than their total length, which could be $$\varTheta (n\cdot d)$$ . In particular, we consider following types queries: reporting and counting all $$T[i \mathinner {.\,.}j]$$ distinct occur show how construct, $$O((n+d) \log ^{O(1)} n)$$ time, structure answers these time $$O(\log n+| output |)$$ case much more involved needs combination locally consistent parsing with orthogonal range searching. Reporting patterns, on other hand, uses maximal repetitions strings. Finally, provide tight—up subpolynomial factors—upper lower bounds for dynamic dictionary.