Shortest Unique Substring Query Revisited

Abstract

We revisit the problem of finding shortest unique substring (SUS) proposed recently by Pei et al. (ICDE’13). We propose an optimal O(n) time and space algorithm that can find an SUS for every location of a string of size n and thus significantly improve their O(n ²) time complexity. Our method also supports finding all the SUSes covering every location, whereas theirs can find only one SUS for every location. Further, our solution is simpler and easier to implement and can also be more space efficient in practice, since we only use the inverse suffix array and the longest common prefix array of the string, while their algorithm uses the suffix tree of the string and other auxiliary data structures. Our theoretical results are validated by an empirical study that shows our method is much faster and more space-saving.

Part of the work was done while the first and the third authors were with TÜBİTAK-BİLGEM-UEKAE Mathematical and Computational Sciences Labs in 2013 summer. All missed proofs and pseudocode can be found in the full version of this paper [2].