Faster Text Fingerprinting

Let s = s1..sn be a text (or sequence) on a finite alphabet Σ. A fingerprint in s is the set of distinct characters contained in one of its substrings. Fingerprinting a text consists of computing the set F of all fingerprints of all its substrings. A fingerprint, f ∈ F , admits a number of maximal locations 〈i, j〉 in S, that is the alphabet of si..sj is f and si−1, sj+1, if defined, are not in f . The set of maximal locations is L, |L| ≤ n|Σ|. Two maximal locations 〈i, j〉 and 〈k, l〉 such that si..sj = sk..sl are named copies and the quotient of L according to the copy relation is named LC . The faster algorithm to compute all fingerprints in s runs in O(n+ |L| log |Σ|) time. We present a quite always faster O((n+ |LC |) log |Σ|) algorithm.