On Longest Repeat Queries

Repeat finding in strings has important applications in subfields such as computational biology. Surprisingly, all prior work on repeat finding did not consider the constraint on the locality of repeats. In this paper, we propose and study the problem of finding longest repetitive substrings covering particular string positions. We propose an $O(n)$ time and space algorithm for finding the longest repeat covering every position of a string of size $n$. Our work is optimal since the reading and the storage of an input string of size $n$ takes $O(n)$ time and space. Because any substring of a repeat is also a repeat, our solution to longest repeat queries effectively provides a "stabbing" tool for practitioners for finding most of the repeats that cover particular string positions.