New Algorithms for Text Fingerprinting

Abstract

Let s = s ₁ .. s _n 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 ${\mathcal{F}}$ of all fingerprints of all its substrings and being able to efficiently answer several questions on this set. A given fingerprint $f \in {\mathcal{F}}$ is represented by a binary array, F, of size |Σ| named a fingerprint table. A fingerprint, $f \in {\mathcal{F}}$, admits a number of maximal locations (i,j) in S, that is the alphabet of s _i .. s _j is f and s _{i − − 1}, s _j + 1, if defined, are not in f. The total number of maximal locations is ${\mathcal{L}} \leq n |\Sigma|+1.$ We present new algorithms and a new data structure for the three problems: (1) compute ${\mathcal{F}}$; (2) given F, answer if F represents a fingerprint in ${\mathcal{F}}$; (3) given F, find all maximal locations of F in s. These problems are respectively solved in $O(({\mathcal{L}}+ n) \log |\Sigma|)$, Θ(|Σ|), and Θ(|Σ| + K) time – where K is the number of maximal locations of F.