In-place algorithms for exact and approximate shortest unique substring problems

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, each of ⌈log2⁡(n)⌉ bits, 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(n2) 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. Experimental study shows that the peak memory usage of our proposal is consistently 9n bytes for any string of size n, validating the claim that our solution is in-place. Further, our proposal uses much less memory and is much faster than the currently best work that has implementation for exact SUS finding.