Efficient Computation of Substring Equivalence Classes with Suffix Arrays

This paper considers enumeration of substring equivalence classes introduced by Blumer et al. (J ACM 34(3):578–595, 1987). These equivalence classes were originally proposed to define a text indexing structure called compact directed acyclic word graphs (CDAWGs). These equivalence classes are also useful for text analysis, since they group together redundant substrings with essentially identical occurrences. In this paper, we present how to enumerate these equivalence classes using only suffix arrays and two auxiliary arrays (rank arrays and lcp arrays), in O(n) time for a given string of length n over the integer alphabet. The proposed method overcomes all the existing algorithms which require $O(nlog\mathit{\sigma })$ time, where $\mathit{\sigma }$ is the alphabet size. Our experimental results show that the proposed method is also practically faster and more memory efficient than the existing ones. Furthermore, we propose an O(n)‐time algorithm which constructs the CDAWG of an input string over the integer alphabet. This algorithm is based on the above‐mentioned algorithm to enumerate equivalence classes. Our experiments show that the proposed method runs faster than the existing algorithm on large alphabets.