Space Efficient Construction of Lyndon Arrays in Linear Time

TL;DR

This paper introduces the first linear-time algorithms for constructing Lyndon arrays with significantly reduced space requirements, outperforming previous methods in efficiency and memory usage.

Contribution

The paper presents novel linear-time algorithms for Lyndon array construction that use minimal extra space, improving upon all prior approaches.

Findings

Algorithms run in linear time.

Significantly lower space consumption than previous methods.

Outperform existing algorithms by an order of magnitude in practice.

Abstract

We present the first linear time algorithm to construct the $2n$-bit version of the Lyndon array for a string of length $n$ using only $o(n)$ bits of working space. A simpler variant of this algorithm computes the plain ($n\lg n$-bit) version of the Lyndon array using only $\mathcal{O}(1)$ words of additional working space. All previous algorithms are either not linear, or use at least $n\lg n$ bits of additional working space. Also in practice, our new algorithms outperform the previous best ones by an order of magnitude, both in terms of time and space.