An In-place Framework for Exact and Approximate Shortest Unique Substring Queries

Abstract: We revisit the exact shortest unique substring (SUS) finding problem, and propose its approximate version where mismatches are allowed, due to its applications in subfields such as computational biology. We design a generic in-place framework that fits to solve both the exact and approximate $k$-mismatch SUS finding, using the minimum $2n$ memory words plus $n$ bytes space, where $n$ is the input string size. By using the in-place framework, we can find the exact and approximate $k$-mismatch SUS for every string position using a total of $O(n)$ and $O(n^2)$ time, respectively, regardless of the value of $k$. Our framework does not involve any compressed or succinct data structures and thus is practical and easy to implement.