Computing All Distinct Squares in Linear Time for Integer Alphabets

TL;DR

This paper introduces a linear-time algorithm for finding all distinct squares in a string over an integer alphabet, and applies it to efficiently compute suffix tree topology and related data structures.

Contribution

It presents the first linear-time algorithm for all distinct squares in strings over integer alphabets, with applications to suffix tree topology and compressed data structures.

Findings

Linear-time computation of all distinct squares

Efficient suffix tree topology construction

Compressed representation of longest previous table

Abstract

Given a string on an integer alphabet, we present an algorithm that computes the set of all distinct squares belonging to this string in time linear to the string length. As an application, we show how to compute the tree topology of the minimal augmented suffix tree in linear time. Asides from that, we elaborate an algorithm computing the longest previous table in a succinct representation using compressed working space.