Space-Efficient Construction of Compressed Indexes in Deterministic Linear Time

TL;DR

This paper presents a method to construct compressed suffix arrays and trees in linear time using space proportional to the input size, improving efficiency over previous algorithms that were slower or used more space.

Contribution

It introduces a deterministic linear-time algorithm for building compressed suffix structures with optimal space complexity, advancing the state of the art.

Findings

Constructed compressed suffix array and tree in O(n) time

Achieved linear-time LZ77 and LZ78 parsing algorithms

Reduced space usage to O(n log σ) bits

Abstract

We show that the compressed suffix array and the compressed suffix tree of a string $T$ can be built in $O(n)$ deterministic time using $O(n\log\sigma)$ bits of space, where $n$ is the string length and $\sigma$ is the alphabet size. Previously described deterministic algorithms either run in time that depends on the alphabet size or need $\omega(n\log \sigma)$ bits of working space. Our result has immediate applications to other problems, such as yielding the first linear-time LZ77 and LZ78 parsing algorithms that use $O(n \log\sigma)$ bits.