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

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.