Various improvements to text fingerprinting

TL;DR

This paper introduces new algorithms and data structures to efficiently compute and query all fingerprints of substrings within a text, addressing problems of enumeration, membership, and localization of fingerprints.

Contribution

It presents novel exact and approximate methods for computing fingerprints, checking fingerprint existence, and locating all maximal occurrences in the text.

Findings

Algorithms for computing all fingerprints are more efficient.

Data structures enable fast fingerprint membership queries.

Methods improve performance for substring fingerprint analysis.

Abstract

Let s = s_1 .. s_n be a text (or sequence) on a finite alphabet \Sigma of size \sigma. A fingerprint in s is the set of distinct characters appearing in one of its substrings. The problem considered here is to compute the set {\cal F} of all fingerprints of all substrings of s in order to answer efficiently certain questions on this set. A substring s_i .. s_j is a maximal location for a fingerprint f in F (denoted by <i,j>) if the alphabet of s_i .. s_j is f and s_{i-1}, s_{j+1}, if defined, are not in f. The set of maximal locations ins is {\cal L} (it is easy to see that |{\cal L}| \leq n \sigma). Two maximal locations <i,j> and <k,l> such that s_i .. s_j = s_k .. s_l are named {\em copies}, and the quotient set of {\cal L} according to the copy relation is denoted by {\cal L}_C. We present new exact and approximate efficient algorithms and data structures for the following three problems: (1) to compute {\cal F}; (2) given f as a set of distinct characters in \Sigma, to answer if f represents a fingerprint in {\cal F}; (3) given f, to find all maximal locations of f in s.